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Afraimovich, Valentin S.

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Author ID: afraimovich.valentin-s Recent zbMATH articles by "Afraimovich, Valentin S."
Published as: Afraimovich, Valentin; Afraimovich, V. S.; Afrajmovich, V. S.; Afraimovich, V.; Afraimovich, Valentin S.; Afraĭmovich, V. S.; Afraimovich, Valentine; Afrajmovich, V.
Homepage: http://www.iico.uaslp.mx/Paginas/Valentin_Afraimovich.aspx
External Links: MGP · Wikidata · dblp · IdRef
Documents Indexed: 111 Publications since 1970, including 4 Books
6 Contributions as Editor
1 Further Contribution
Biographic References: 3 Publications
all top 5

Co-Authors

5 single-authored
16 Shilnikov, Leonid Pavlovich
15 Rabinovich, Mikhail I.
7 Bunimovich, Leonid Abramovich
7 Urías, Jesús
7 Young, Todd R.
6 Lerman, Lev
6 Nekorkin, Vladimir I.
6 Pesin, Yakov Borisovich
6 Shereshevsky, Mark A.
5 Chazottes, Jean-René
5 Ugalde, Edgardo
4 Glebsky, Lev Yu.
4 Gonchenko, Sergey V.
4 Varona, Pablo
3 Babin, A.
3 Bykov, V. V.
3 Chow, Shui-Nee
3 Ilyashenko, Yulij Sergeevich
3 Luo, Albert C. J.
3 Shilnikov, Andrey L.
3 Turaev, Dmitry V.
3 Zaslavskiĭ, Georgiĭ Moiseevich
2 Aranson, Igor S.
2 Arnol’d, Vladimir Igorevich
2 Cordonet, A.
2 Courbage, Maurice
2 Hsu, Szebi
2 Huerta, Ramón
2 Lin, Wen-Wei
2 Muezzinoglu, Mehmet K.
2 Saussol, Benoît
2 Tristan, Irma
2 Vazquez, Rosendo
2 Zheleznyak, Alexander L.
2 Zheleznyak, I. L.
1 Anosov, Dmitriĭ Viktorovich
1 Belyakov, Leonid A.
1 Chernov, Nikolai Ivanovich
1 Cuevas, Dario
1 Dmitrichev, A. S.
1 Dmitrichev, Aleksei
1 Ezersky, Alexander B.
1 Fernandez, Bastien
1 Fu, Xilin
1 Gelover-Santiago, A. L.
1 Glebskij, L. Ya.
1 Gong, Xue
1 Grines, Vyacheslav Zigmundovich
1 Hale, Jack Kenneth
1 Kasatkin, D. V.
1 Kashchenko, Sergeĭ Aleksandrovich
1 Katok, Anatole B.
1 Kozlov, Valeriĭ Vasil’evich
1 Lin, Hueyer
1 Liu, Weishi
1 Maass, Alejandro
1 Machado, José António Tenreiro
1 Morante, Antonio
1 Moreno, S. V.
1 Morozov, Al’bert Dmitrievich
1 Moses, Gregory A.
1 Neĭshtadt, Anatoliĭ Iserovich
1 Ordaz, F. C.
1 Osipov, Grigory V.
1 Ramírez, Leticia
1 Rechtman, Raúl
1 Rodrigues, Hildebrando Munhoz
1 Rulkov, Nikolai F.
1 Samoĭlenko, Anatoliĭ Mykhaĭlovych
1 Sataev, Evgueni A.
1 Shalfeev, Vladimir D.
1 Sharkovs’kyĭ, Oleksandr Mykolaĭovych
1 Shchapin, Dmitry S.
1 Shen, Wenxian
1 Sinaĭ, Yakov Grigor’evich
1 Tempel’man, Arkadĭ Aleksandrovich
1 Treshchev, Dmitriĭ Valer’evich
1 Vozovoj, L. P.
1 Zhang, Jiazhong
1 Zhigulin, V. P.
all top 5

Serials

14 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
10 Nonlinearity
10 Chaos
5 Discrete and Continuous Dynamical Systems
3 Russian Mathematical Surveys
3 Soviet Mathematics. Doklady
3 Selecta Mathematica Sovietica
3 Physica D
3 Taiwanese Journal of Mathematics
3 Regular and Chaotic Dynamics
3 Communications in Nonlinear Science and Numerical Simulation
2 Journal of Applied Mathematics and Mechanics
2 Soviet Scientific Reviews. Section C
2 Transactions of the Moscow Mathematical Society
2 Trudy Moskovskogo Matematicheskogo Obshchestva
2 Random & Computational Dynamics
2 Far East Journal of Dynamical Systems
2 Dynamical Systems
2 Discrete and Continuous Dynamical Systems. Series B
2 Nonlinear Systems and Complexity
2 Discontinuity, Nonlinearity, and Complexity
2 Nonlinear Physical Science
1 Biological Cybernetics
1 Physics Letters. A
1 Uspekhi Matematicheskikh Nauk [N. S.]
1 Bulletin of Mathematical Biology
1 Mathematics of the USSR. Izvestiya
1 Transactions of the American Mathematical Society
1 Dynamics and Stability of Systems
1 Dynamic Systems and Applications
1 Soviet Physics. Doklady
1 Journal of Dynamics and Differential Equations
1 Communications in Analysis and Geometry
1 Electronic Research Announcements of the American Mathematical Society
1 Journal of Dynamical and Control Systems
1 Matematicheskoe Modelirovanie
1 Translations. Series 2. American Mathematical Society
1 World Scientific Series on Nonlinear Science. Series A
1 AMS/IP Studies in Advanced Mathematics
1 Monograph Series on Nonlinear Science and Complexity

Publications by Year

Citations contained in zbMATH Open

79 Publications have been cited 697 times in 400 Documents Cited by Year
Chaos of travelling waves in a discrete chain of diffusively coupled maps. Zbl 0870.58049
Afraimovich, V. S.; Nekorkin, V. I.
53
1994
Lectures on chaotic dynamical systems. Zbl 1152.37300
Afraimovich, Valentin; Hsu, Sze-Bi
41
2003
Synchronization in lattices of coupled oscillators. Zbl 1194.34056
Afraimovich, V. S.; Chow, S.-N.; Hale, J. K.
38
1997
On attracting structurally unstable limit sets of Lorenz attractor type. Zbl 0506.58023
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
34
1982
Invariant two-dimensional tori, their breakdown and stochasticity. Zbl 0751.58024
Afrajmovich, V. S.; Shil’nikov, L. P.
31
1991
On the origin of reproducible sequential activity in neural circuits. Zbl 1080.37100
Afraimovich, V. S.; Zhigulin, V. P.; Rabinovich, M. I.
28
2004
On structurally unstable attracting limit sets of Lorenz attractor type. Zbl 0527.58024
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
26
1983
Heteroclinic contours in neural ensembles and the winnerless competition principle. Zbl 1099.37518
Afraimovich, Valentin S.; Rabinovich, Mikhail I.; Varona, Pablo
25
2004
Stability, structures and chaos in nonlinear synchronization networks. Ed. by A. V. Gaponov-Grekhov and M. I. Rabinovich. Zbl 0845.93003
Afraimovich, V. S.; Nekorkin, V. I.; Osipov, G. V.; Shalfeev, V. D.
24
1994
On the origin and structure of the Lorenz attractor. Zbl 0451.76052
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
19
1977
Pesin’s dimension for Poincaré recurrences. Zbl 0933.37019
Afraimovich, V.
19
1997
Synchronization in lattices of coupled oscillators with Neumann/periodic boundary conditions. Zbl 1067.34052
Afraimovich, V. S.; Lin, Wen-Wei
15
1998
Uniform dissipativeness and synchronization on nonautonomous equations. Zbl 0964.34040
Afraimovich, Valentine; Rodrigues, Hildebrando M.
13
1998
Strange attractors and quasiattractors. Zbl 0532.58018
Afrajmovich, V. S.; Shil’nikov, L. P.
13
1983
Travelling waves in lattice models of multi-dimensional and multi- component media. I: General hyperbolic properties. Zbl 0773.76006
Afrajmovich, V.; Pesin, Ya
12
1993
Pointwise dimensions for Poincaré recurrences associated with maps and special flows. Zbl 1029.37007
Afraimovich, Valentin; Chazottes, Jean René; Saussol, Benoît
11
2003
Dynamical networks: interplay of topology, interactions and local dynamics. Zbl 1124.37008
Afraimovich, V. S.; Bunimovich, L. A.
11
2007
Which hole is leaking the most: a topological approach to study open systems. Zbl 1186.37015
Afraimovich, V. S.; Bunimovich, L. A.
11
2010
Scientific heritage of L. P. Shilnikov. Zbl 1353.37001
Afraimovich, Valentin S.; Gonchenko, Sergey V.; Lerman, Lev M.; Shilnikov, Andrey L.; Turaev, Dmitry V.
11
2014
Topological properties of linearly coupled expanding map lattices. Zbl 0983.37100
Afraimovich, Valentin; Fernandez, Bastien
10
2000
Bifurcation theory. Zbl 0797.58003
Arnol’d, V. I.; Afrajmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
10
1986
Long-range interactions, stochasticity and fractional dynamics. Dedicated to George M. Zaslavsky (1935-2008). Zbl 1209.70002
9
2010
Chaotic behavior of three competing species of May-Leonard model under small periodic perturbations. Zbl 1090.92508
Afraimovich, Valentin S.; Hsu, Sze-Bi; Lin, Huey-Er
9
2001
Statistical properties of 2-D generalized hyperbolic attractors. Zbl 1055.37526
Afraĭmovich, V. S.; Chernov, N. I.; Sataev, E. A.
9
1995
Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model. Zbl 1309.92064
Afraimovich, Valentin; Tristan, Irma; Huerta, Ramon; Rabinovich, Mikhail I.
9
2008
Bifurcation theory and catastrophe theory. Translated from the 1986 Russian original by N. D. Kazarinoff. Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences (Dynamical systems V), 5 (1994). Zbl 1038.37500
Arnold, V. I.; Afraĭmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
8
1999
Space-time complexity in Hamiltonian dynamics. Zbl 1080.37581
Afraimovich, V.; Zaslavsky, G. M.
8
2003
Generation and reshaping of sequences in neural systems. Zbl 1114.92016
Rabinovich, Mikhail I.; Huerta, Ramón; Varona, Pablo; Afraimovich, Valentin S.
8
2006
On attainable transitions from Morse-Smale systems to systems with many periodic motions. Zbl 0322.58007
Afrajmovich, V. S.; Shil’nikov, L. P.
8
1976
Fractal dimension for Poincaré recurrences as an indicator of synchronized chaotic regimes. Zbl 1090.37509
Afraimovich, Valentin S.; Lin, Wen-Wei; Rulkov, Nikolai F.
7
2000
Lorenz type attractors from codimension one bifurcation. Zbl 0839.34064
Afraimovich, Valentine; Chow, Shui-Nee; Liu, Weishi
7
1995
Density of defects and spatial entropy in extended systems. Zbl 0888.58015
Afraimovich, V. S.; Bunimovich, L. A.
7
1995
Local dimensions for Poincaré recurrences. Zbl 0955.37013
Afraimovich, Valentin; Chazottes, Jean-René; Saussol, Benoît
6
2000
Conventional multipliers for homoclinic orbits. Zbl 0887.58037
Afraimovich, V.; Liu, W. S.; Young, T.
6
1996
Synchronization in directionally coupled systems: Some rigorous results. Zbl 0999.37006
Afraimovich, V.; Chazottes, J.-R.; Cordonet, A.
6
2001
Symbolic dynamics for sticky sets in Hamiltonian systems. Zbl 0979.37002
Afraimovich, Valentin; Maass, Alejandro; Urías, Jesús
6
2000
Traveling waves in lattice models of multidimensional and multicomponent media. II: Ergodic properties and dimension. Zbl 1055.37584
Afraĭmovich, V. S.; Pesin, Ya. B.; Tempelman, A. A.
6
1993
On critical sets of Morse-Smale systems. Zbl 0295.58007
Afraĭmovich, V. S.; Shil’nikov, L. P.
6
1975
On small periodic perturbations of autonomous systems. Zbl 0305.34069
Afraĭmovich, V. S.; Shil’nikov, L. P.
6
1974
Spectra of dimensions for Poincaré recurrences. Zbl 1011.37009
Afraimovich, V.; Schmeling, J.; Ugalde, E.; Urías, J.
5
2000
Stability of spatially homogeneous chaotic regimes in unidirectional chains. Zbl 0712.58041
Aranson, I. S.; Afrajmovich, V. S.; Rabinovich, M. I.
5
1990
Spatial chaotic structure of attractors of reaction-diffusion systems. Zbl 0864.35053
Afraimovich, V.; Babin, A.; Chow, S.-N.
5
1996
Fractal dimensions for Poincaré recurrences. Zbl 1180.37002
Afraimovich, Valentin; Ugalde, Edgardo; Urías, Jesus
5
2006
Dimension of Lorenz type attractors. Zbl 0628.58031
Afrajmovich, V. S.; Pesin, Ya. B.
5
1987
Simplest structures in coupled map lattices and their stability. Zbl 0810.34036
Afraimovich, V. S.; Bunimovich, L. A.
5
1993
Two-dimensional heteroclinic attractor in the generalized Lotka-Volterra system. Zbl 1342.34073
Afraimovich, Valentin S.; Moses, Gregory; Young, Todd
5
2016
Sticky orbits of chaotic Hamiltonian dynamics. Zbl 0929.37020
Afraimovich, V.; Zaslavsky, G. M.
4
1998
On the density of directional entropy in lattice dynamical systems. Zbl 1083.37057
Afraimovich, V.; Morante, A.; Ugalde, E.
4
2004
Heteroclinic binding. Zbl 1204.37089
Rabinovich, Mikhail I.; Afraimovich, Valentin S.; Varona, Pablo
4
2010
The ring principle in problems of interaction between two self- oscillating systems. Zbl 0404.70016
Afrajmovich, V. S.; Shil’nikov, L. P.
4
1978
On the singular sets of Morse-Smale systems. (Über die kritischen Mengen eines Morse-Smale Systems.) Zbl 0276.58008
Afraĭmovich, V. S.; Shil’nikov, L. P.
4
1973
Existence of evolution operators group for infinite lattice of coupled ordinary differential equation. Zbl 0802.34013
Afraimovich, V. S.; Chow, Shui-Nee
4
1994
Bipermutative cellular automata are topologically conjugate to the one- sided Bernoulli shift. Zbl 0780.28011
Shereshevsky, M. A.; Afrajmovich, V. S.
3
1993
Symbolic dynamics in multidimensional annulus and chimera states. Zbl 1300.37010
Afraimovich, V. S.; Shilnikov, L. P.
3
2014
Sequential dynamics of master-slave systems. Zbl 1278.37057
Afraimovich, Valentin; Cuevas, Dario; Young, Todd
3
2013
On some global bifurcations connected with the disappearance of a fixed point of saddle-node type. Zbl 0312.34035
Afrajmovich, V. S.; Shil’nikov, L. P.
3
1974
Measures related to \((\varepsilon,n)\)-complexity functions. Zbl 1177.28035
Afraimovich, Valentin; Glebsky, Lev
3
2008
Hierarchical heteroclinics in dynamical model of cognitive processes: chunking. Zbl 1302.92016
Afraimovich, Valentin S.; Young, Todd R.; Rabinovich, Mikhail I.
3
2014
On a bifurcation of codimension 1 leading to the appearance of a countable set of tori. Zbl 0509.58033
Afrajmovich, V. S.; Shil’nikov, L. P.
3
1982
Sequential memory: binding dynamics. Zbl 1374.92022
Afraimovich, Valentin; Gong, Xue; Rabinovich, Mikhail
3
2015
Spectrum of dimensions for escape time. Zbl 1334.37014
Afraimovich, Valentin; Vazquez, Rosendo
2
2013
Nonsmooth functions in generalized synchronization of chaos. Zbl 0984.37056
Afraimovich, V.; Chazottes, J.-R.; Cordonet, A.
2
2001
Dynamical description of spatial disorder. Zbl 1194.37129
Afraimovich, V. S.; Ezersky, A. B.; Rabinovich, M. I.; Shereshevsky, M. A.; Zheleznyak, A. L.
2
1992
Dynamical networks: continuous time and general discrete time models. Zbl 1213.37021
Afraimovich, V. S.; Bunimovich, L. A.; Moreno, S. V.
2
2010
Working with complexity functions. Zbl 1136.37312
Zaslavsky, G. M.; Afraimovich, V.
2
2005
The mechanism of the hard appearance of a two-frequency oscillation mode in the case of Andronov-Hopf reverse bifurcation. Zbl 0731.58050
Afrajmovich, V. S.; Vozovoj, L. P.
2
1989
Hyperbolic homoclinic points of \(\mathbb{Z}^ d\)-actions in lattice dynamical systems. Zbl 0874.58064
Afraimovich, V. S.; Chow, Shu-Nee; Shen, Wenxian
2
1996
Relating the sequential dynamics of excitatory neural networks to synaptic cellular automata. Zbl 1317.92013
Nekorkin, V. I.; Dmitrichev, A. S.; Kasatkin, D. V.; Afraimovich, V. S.
2
2011
Nonlinear dynamics of emotion-cognition interaction: When emotion does not destroy cognition? Zbl 1221.92016
Afraimovich, Valentin; Young, Todd; Muezzinoglu, Mehmet K.; Rabinovich, Mikhail I.
2
2011
Mind-to-mind heteroclinic coordination: model of sequential episodic memory initiation. Zbl 1414.37035
Afraimovich, V. S.; Zaks, M. A.; Rabinovich, M. I.
1
2018
Infinitely spatially complex solutions of PDE and their homotopy complexity. Zbl 0994.35048
Afraimovich, V.; Babin, A.; Chow, S.-N.
1
2001
Dimension-like characteristics of invariant sets in dynamical systems. Zbl 1031.37024
Afraimovich, Valentin; Urias, Jesus
1
2002
Spectra of dimensions for Poincaré recurrences for special flows. Zbl 1140.37308
Afraimovich, V.; Chazottes, J.-R.; Ugalde, E.
1
2002
Hyperbolicity of infinite-dimensional drift systems. Zbl 0765.58024
Afrajmovich, V. S.; Pesin, Ya. B.
1
1990
On smooth changes of variables. Zbl 0727.58027
Afrajmovich, V. S.
1
1990
Measures of \(\varepsilon\)-complexity. Zbl 1094.28008
Afraimovich, V.; Glebsky, L.
1
2005
The Hausdorff dimension of attractors appearing by saddle-node bifurcations. Zbl 0874.58037
Afraimovich, V. S.; Shereshevskij, M. A.
1
1991
A class of cellular automata modeling winnerless competition. Zbl 1080.37503
Afraimovich, V.; Ordaz, F. C.; Urías, J.
1
2002
Directional complexity and entropy for lift mappings. Zbl 1358.37076
Afraimovich, Valentin; Courbage, Maurice; Glebsky, Lev
1
2015
Mind-to-mind heteroclinic coordination: model of sequential episodic memory initiation. Zbl 1414.37035
Afraimovich, V. S.; Zaks, M. A.; Rabinovich, M. I.
1
2018
Two-dimensional heteroclinic attractor in the generalized Lotka-Volterra system. Zbl 1342.34073
Afraimovich, Valentin S.; Moses, Gregory; Young, Todd
5
2016
Sequential memory: binding dynamics. Zbl 1374.92022
Afraimovich, Valentin; Gong, Xue; Rabinovich, Mikhail
3
2015
Directional complexity and entropy for lift mappings. Zbl 1358.37076
Afraimovich, Valentin; Courbage, Maurice; Glebsky, Lev
1
2015
Scientific heritage of L. P. Shilnikov. Zbl 1353.37001
Afraimovich, Valentin S.; Gonchenko, Sergey V.; Lerman, Lev M.; Shilnikov, Andrey L.; Turaev, Dmitry V.
11
2014
Symbolic dynamics in multidimensional annulus and chimera states. Zbl 1300.37010
Afraimovich, V. S.; Shilnikov, L. P.
3
2014
Hierarchical heteroclinics in dynamical model of cognitive processes: chunking. Zbl 1302.92016
Afraimovich, Valentin S.; Young, Todd R.; Rabinovich, Mikhail I.
3
2014
Sequential dynamics of master-slave systems. Zbl 1278.37057
Afraimovich, Valentin; Cuevas, Dario; Young, Todd
3
2013
Spectrum of dimensions for escape time. Zbl 1334.37014
Afraimovich, Valentin; Vazquez, Rosendo
2
2013
Relating the sequential dynamics of excitatory neural networks to synaptic cellular automata. Zbl 1317.92013
Nekorkin, V. I.; Dmitrichev, A. S.; Kasatkin, D. V.; Afraimovich, V. S.
2
2011
Nonlinear dynamics of emotion-cognition interaction: When emotion does not destroy cognition? Zbl 1221.92016
Afraimovich, Valentin; Young, Todd; Muezzinoglu, Mehmet K.; Rabinovich, Mikhail I.
2
2011
Which hole is leaking the most: a topological approach to study open systems. Zbl 1186.37015
Afraimovich, V. S.; Bunimovich, L. A.
11
2010
Long-range interactions, stochasticity and fractional dynamics. Dedicated to George M. Zaslavsky (1935-2008). Zbl 1209.70002
9
2010
Heteroclinic binding. Zbl 1204.37089
Rabinovich, Mikhail I.; Afraimovich, Valentin S.; Varona, Pablo
4
2010
Dynamical networks: continuous time and general discrete time models. Zbl 1213.37021
Afraimovich, V. S.; Bunimovich, L. A.; Moreno, S. V.
2
2010
Winnerless competition principle and prediction of the transient dynamics in a Lotka-Volterra model. Zbl 1309.92064
Afraimovich, Valentin; Tristan, Irma; Huerta, Ramon; Rabinovich, Mikhail I.
9
2008
Measures related to \((\varepsilon,n)\)-complexity functions. Zbl 1177.28035
Afraimovich, Valentin; Glebsky, Lev
3
2008
Dynamical networks: interplay of topology, interactions and local dynamics. Zbl 1124.37008
Afraimovich, V. S.; Bunimovich, L. A.
11
2007
Generation and reshaping of sequences in neural systems. Zbl 1114.92016
Rabinovich, Mikhail I.; Huerta, Ramón; Varona, Pablo; Afraimovich, Valentin S.
8
2006
Fractal dimensions for Poincaré recurrences. Zbl 1180.37002
Afraimovich, Valentin; Ugalde, Edgardo; Urías, Jesus
5
2006
Working with complexity functions. Zbl 1136.37312
Zaslavsky, G. M.; Afraimovich, V.
2
2005
Measures of \(\varepsilon\)-complexity. Zbl 1094.28008
Afraimovich, V.; Glebsky, L.
1
2005
On the origin of reproducible sequential activity in neural circuits. Zbl 1080.37100
Afraimovich, V. S.; Zhigulin, V. P.; Rabinovich, M. I.
28
2004
Heteroclinic contours in neural ensembles and the winnerless competition principle. Zbl 1099.37518
Afraimovich, Valentin S.; Rabinovich, Mikhail I.; Varona, Pablo
25
2004
On the density of directional entropy in lattice dynamical systems. Zbl 1083.37057
Afraimovich, V.; Morante, A.; Ugalde, E.
4
2004
Lectures on chaotic dynamical systems. Zbl 1152.37300
Afraimovich, Valentin; Hsu, Sze-Bi
41
2003
Pointwise dimensions for Poincaré recurrences associated with maps and special flows. Zbl 1029.37007
Afraimovich, Valentin; Chazottes, Jean René; Saussol, Benoît
11
2003
Space-time complexity in Hamiltonian dynamics. Zbl 1080.37581
Afraimovich, V.; Zaslavsky, G. M.
8
2003
Dimension-like characteristics of invariant sets in dynamical systems. Zbl 1031.37024
Afraimovich, Valentin; Urias, Jesus
1
2002
Spectra of dimensions for Poincaré recurrences for special flows. Zbl 1140.37308
Afraimovich, V.; Chazottes, J.-R.; Ugalde, E.
1
2002
A class of cellular automata modeling winnerless competition. Zbl 1080.37503
Afraimovich, V.; Ordaz, F. C.; Urías, J.
1
2002
Chaotic behavior of three competing species of May-Leonard model under small periodic perturbations. Zbl 1090.92508
Afraimovich, Valentin S.; Hsu, Sze-Bi; Lin, Huey-Er
9
2001
Synchronization in directionally coupled systems: Some rigorous results. Zbl 0999.37006
Afraimovich, V.; Chazottes, J.-R.; Cordonet, A.
6
2001
Nonsmooth functions in generalized synchronization of chaos. Zbl 0984.37056
Afraimovich, V.; Chazottes, J.-R.; Cordonet, A.
2
2001
Infinitely spatially complex solutions of PDE and their homotopy complexity. Zbl 0994.35048
Afraimovich, V.; Babin, A.; Chow, S.-N.
1
2001
Topological properties of linearly coupled expanding map lattices. Zbl 0983.37100
Afraimovich, Valentin; Fernandez, Bastien
10
2000
Fractal dimension for Poincaré recurrences as an indicator of synchronized chaotic regimes. Zbl 1090.37509
Afraimovich, Valentin S.; Lin, Wen-Wei; Rulkov, Nikolai F.
7
2000
Local dimensions for Poincaré recurrences. Zbl 0955.37013
Afraimovich, Valentin; Chazottes, Jean-René; Saussol, Benoît
6
2000
Symbolic dynamics for sticky sets in Hamiltonian systems. Zbl 0979.37002
Afraimovich, Valentin; Maass, Alejandro; Urías, Jesús
6
2000
Spectra of dimensions for Poincaré recurrences. Zbl 1011.37009
Afraimovich, V.; Schmeling, J.; Ugalde, E.; Urías, J.
5
2000
Bifurcation theory and catastrophe theory. Translated from the 1986 Russian original by N. D. Kazarinoff. Reprint of the original English edition from the series Encyclopaedia of Mathematical Sciences (Dynamical systems V), 5 (1994). Zbl 1038.37500
Arnold, V. I.; Afraĭmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
8
1999
Synchronization in lattices of coupled oscillators with Neumann/periodic boundary conditions. Zbl 1067.34052
Afraimovich, V. S.; Lin, Wen-Wei
15
1998
Uniform dissipativeness and synchronization on nonautonomous equations. Zbl 0964.34040
Afraimovich, Valentine; Rodrigues, Hildebrando M.
13
1998
Sticky orbits of chaotic Hamiltonian dynamics. Zbl 0929.37020
Afraimovich, V.; Zaslavsky, G. M.
4
1998
Synchronization in lattices of coupled oscillators. Zbl 1194.34056
Afraimovich, V. S.; Chow, S.-N.; Hale, J. K.
38
1997
Pesin’s dimension for Poincaré recurrences. Zbl 0933.37019
Afraimovich, V.
19
1997
Conventional multipliers for homoclinic orbits. Zbl 0887.58037
Afraimovich, V.; Liu, W. S.; Young, T.
6
1996
Spatial chaotic structure of attractors of reaction-diffusion systems. Zbl 0864.35053
Afraimovich, V.; Babin, A.; Chow, S.-N.
5
1996
Hyperbolic homoclinic points of \(\mathbb{Z}^ d\)-actions in lattice dynamical systems. Zbl 0874.58064
Afraimovich, V. S.; Chow, Shu-Nee; Shen, Wenxian
2
1996
Statistical properties of 2-D generalized hyperbolic attractors. Zbl 1055.37526
Afraĭmovich, V. S.; Chernov, N. I.; Sataev, E. A.
9
1995
Lorenz type attractors from codimension one bifurcation. Zbl 0839.34064
Afraimovich, Valentine; Chow, Shui-Nee; Liu, Weishi
7
1995
Density of defects and spatial entropy in extended systems. Zbl 0888.58015
Afraimovich, V. S.; Bunimovich, L. A.
7
1995
Chaos of travelling waves in a discrete chain of diffusively coupled maps. Zbl 0870.58049
Afraimovich, V. S.; Nekorkin, V. I.
53
1994
Stability, structures and chaos in nonlinear synchronization networks. Ed. by A. V. Gaponov-Grekhov and M. I. Rabinovich. Zbl 0845.93003
Afraimovich, V. S.; Nekorkin, V. I.; Osipov, G. V.; Shalfeev, V. D.
24
1994
Existence of evolution operators group for infinite lattice of coupled ordinary differential equation. Zbl 0802.34013
Afraimovich, V. S.; Chow, Shui-Nee
4
1994
Travelling waves in lattice models of multi-dimensional and multi- component media. I: General hyperbolic properties. Zbl 0773.76006
Afrajmovich, V.; Pesin, Ya
12
1993
Traveling waves in lattice models of multidimensional and multicomponent media. II: Ergodic properties and dimension. Zbl 1055.37584
Afraĭmovich, V. S.; Pesin, Ya. B.; Tempelman, A. A.
6
1993
Simplest structures in coupled map lattices and their stability. Zbl 0810.34036
Afraimovich, V. S.; Bunimovich, L. A.
5
1993
Bipermutative cellular automata are topologically conjugate to the one- sided Bernoulli shift. Zbl 0780.28011
Shereshevsky, M. A.; Afrajmovich, V. S.
3
1993
Dynamical description of spatial disorder. Zbl 1194.37129
Afraimovich, V. S.; Ezersky, A. B.; Rabinovich, M. I.; Shereshevsky, M. A.; Zheleznyak, A. L.
2
1992
Invariant two-dimensional tori, their breakdown and stochasticity. Zbl 0751.58024
Afrajmovich, V. S.; Shil’nikov, L. P.
31
1991
The Hausdorff dimension of attractors appearing by saddle-node bifurcations. Zbl 0874.58037
Afraimovich, V. S.; Shereshevskij, M. A.
1
1991
Stability of spatially homogeneous chaotic regimes in unidirectional chains. Zbl 0712.58041
Aranson, I. S.; Afrajmovich, V. S.; Rabinovich, M. I.
5
1990
Hyperbolicity of infinite-dimensional drift systems. Zbl 0765.58024
Afrajmovich, V. S.; Pesin, Ya. B.
1
1990
On smooth changes of variables. Zbl 0727.58027
Afrajmovich, V. S.
1
1990
The mechanism of the hard appearance of a two-frequency oscillation mode in the case of Andronov-Hopf reverse bifurcation. Zbl 0731.58050
Afrajmovich, V. S.; Vozovoj, L. P.
2
1989
Dimension of Lorenz type attractors. Zbl 0628.58031
Afrajmovich, V. S.; Pesin, Ya. B.
5
1987
Bifurcation theory. Zbl 0797.58003
Arnol’d, V. I.; Afrajmovich, V. S.; Il’yashenko, Yu. S.; Shil’nikov, L. P.
10
1986
On structurally unstable attracting limit sets of Lorenz attractor type. Zbl 0527.58024
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
26
1983
Strange attractors and quasiattractors. Zbl 0532.58018
Afrajmovich, V. S.; Shil’nikov, L. P.
13
1983
On attracting structurally unstable limit sets of Lorenz attractor type. Zbl 0506.58023
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
34
1982
On a bifurcation of codimension 1 leading to the appearance of a countable set of tori. Zbl 0509.58033
Afrajmovich, V. S.; Shil’nikov, L. P.
3
1982
The ring principle in problems of interaction between two self- oscillating systems. Zbl 0404.70016
Afrajmovich, V. S.; Shil’nikov, L. P.
4
1978
On the origin and structure of the Lorenz attractor. Zbl 0451.76052
Afrajmovich, V. S.; Bykov, V. V.; Shil’nikov, L. P.
19
1977
On attainable transitions from Morse-Smale systems to systems with many periodic motions. Zbl 0322.58007
Afrajmovich, V. S.; Shil’nikov, L. P.
8
1976
On critical sets of Morse-Smale systems. Zbl 0295.58007
Afraĭmovich, V. S.; Shil’nikov, L. P.
6
1975
On small periodic perturbations of autonomous systems. Zbl 0305.34069
Afraĭmovich, V. S.; Shil’nikov, L. P.
6
1974
On some global bifurcations connected with the disappearance of a fixed point of saddle-node type. Zbl 0312.34035
Afrajmovich, V. S.; Shil’nikov, L. P.
3
1974
On the singular sets of Morse-Smale systems. (Über die kritischen Mengen eines Morse-Smale Systems.) Zbl 0276.58008
Afraĭmovich, V. S.; Shil’nikov, L. P.
4
1973
all top 5

Cited by 590 Authors

24 Afraimovich, Valentin S.
15 Turaev, Dmitry V.
13 Bunimovich, Leonid Abramovich
13 Gonchenko, Sergey V.
12 Rabinovich, Mikhail I.
10 Morales, Carlos Arnoldo
9 Kuznetsov, Sergey P.
9 Nekorkin, Vladimir I.
8 Anishchenko, Vadim Semenovich
8 Fernandez, Bastien
8 Kazakov, Alexey O.
8 Shilnikov, Andrey L.
8 Shilnikov, Leonid Pavlovich
8 Zhou, Shengfan
7 Ashwin, Peter
7 Gonchenko, Alexander S.
7 Rodrigues, Alexandre A. P.
7 Strelkova, Galina Ivanova
7 Tarasov, Vasily E.
6 Courbage, Maurice
6 Young, Todd R.
5 Semenova, Nadezhda Igorevna
4 Boev, Yaroslav Igorevich
4 Chiu, Chuang-Hsiung
4 Coutinho, Ricardo
4 Juang, Jonq
4 Kruglov, Vyacheslav Pavlovich
4 Kurths, Jürgen
4 Labouriau, Isabel S.
4 Lin, Wen-Wei
4 Maslennikov, Oleg V.
4 Mira, Christian
4 Mosekilde, Erik
4 Qin, Wenxin
4 Varona, Pablo
3 Abadi, Miguel Natalio
3 Arbieto, Alexander
3 beim Graben, Peter
3 Bykov, V. V.
3 Carrasco-Olivera, Dante
3 Gu, Anhui
3 Hasler, Martin J.
3 Haydn, Nicolai T. A.
3 Huerta, Ramón
3 Labarca, Rafael
3 Lerman, Lev
3 Osipov, Grigory V.
3 Ovsyannikov, Ivan I.
3 Peng, Chenchang
3 Pesin, Yakov Borisovich
3 Pochinka, Olga Vital’evna
3 Pusuluri, Krishna
3 San Martín Rebolledo, Bernardo
3 Sataev, Igor’ Rustamovich
3 Selverston, Allen I.
3 Urías, Jesús
3 Vaienti, Sandro
3 Zaks, Michael A.
2 Andrievskiĭ, Boris Rostislavich
2 Ban, Jungchao
2 Barrio, Roberto
2 Belykh, Igor V.
2 Belykh, Vladimir N.
2 Bick, Christian
2 Bretas, Newton Geraldo
2 Campos, Eric
2 Chow, Shui-Nee
2 Coombes, Stephen
2 Creaser, Jennifer L.
2 Dawes, Jonathan H. P.
2 Delshams, Amadeu
2 Demers, Mark F.
2 Deng, Bo
2 Dmitrichev, A. S.
2 Evans, Robin J.
2 Fradkov, Aleksandr L’vovich
2 Glebsky, Lev Yu.
2 Gonchenko, Marina S.
2 Govorukhin, Vasily N.
2 Grines, Vyacheslav Zigmundovich
2 Homburg, Ale Jan
2 Hsu, Cheng-Hsiung
2 Huguet, Gemma
2 Klinshpont, N. È.
2 Komarov, Maxim A.
2 Kozlov, A. D.
2 Kuznetsov, Nikolay Vladimirovich
2 Kuznetsov, Yuri Alexandrovich
2 Lambert, Rodrigo
2 Li, Chin-Lung
2 Li, Dongchen
2 Li, Ming-Chia
2 Li, Yangrong
2 Lin, Song-Sun
2 Liu, Weishi
2 Liu, Zengrong
2 Lowenstein, John H.
2 Ma, Jianhua
2 Maistrenko, Yuri L.
2 Makarov, Valeri A.
...and 490 more Authors
all top 5

Cited in 109 Serials

55 Chaos
40 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
38 Physica D
18 Regular and Chaotic Dynamics
14 Communications in Nonlinear Science and Numerical Simulation
12 Journal of Mathematical Analysis and Applications
12 Journal of Differential Equations
9 Dynamical Systems
8 Nonlinearity
8 Chaos, Solitons and Fractals
8 Journal of Dynamics and Differential Equations
7 Journal of Statistical Physics
5 Journal of Applied Mathematics and Mechanics
5 Ergodic Theory and Dynamical Systems
5 Journal of Nonlinear Science
5 Discrete and Continuous Dynamical Systems
4 Computers & Mathematics with Applications
4 Communications in Mathematical Physics
4 Journal of the Franklin Institute
3 Biological Cybernetics
3 Physics Letters. A
3 Proceedings of the American Mathematical Society
3 Transactions of the American Mathematical Society
3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
3 Computational Mathematics and Mathematical Physics
3 Journal of Computational Neuroscience
3 Journal of Difference Equations and Applications
3 Discrete and Continuous Dynamical Systems. Series B
3 Stochastics and Dynamics
3 Bulletin of the Brazilian Mathematical Society. New Series
2 International Journal of Modern Physics B
2 Journal of Fluid Mechanics
2 Journal of Mathematical Biology
2 Journal of Mathematical Physics
2 Physica A
2 Applied Mathematics and Computation
2 Mathematische Annalen
2 Topology and its Applications
2 Neural Computation
2 Japan Journal of Industrial and Applied Mathematics
2 Boletim da Sociedade Brasileira de Matemática. Nova Série
2 Nonlinear Dynamics
2 Journal of Shanghai University
2 Fractional Calculus & Applied Analysis
2 Acta Mathematica Sinica. English Series
2 Advances in Complex Systems
2 SIAM Journal on Applied Dynamical Systems
2 The Journal of Mathematical Neuroscience
2 Journal of Theoretical Biology
2 Nelineĭnaya Dinamika
1 Applicable Analysis
1 Computer Methods in Applied Mechanics and Engineering
1 Computer Physics Communications
1 Communications on Pure and Applied Mathematics
1 International Journal of Engineering Science
1 International Journal of Solids and Structures
1 Israel Journal of Mathematics
1 Journal of the Mechanics and Physics of Solids
1 Mathematical Notes
1 Physics Reports
1 Rocky Mountain Journal of Mathematics
1 Russian Mathematical Surveys
1 Theoretical and Mathematical Physics
1 Bulletin of Mathematical Biology
1 Prikladnaya Matematika i Mekhanika
1 Advances in Mathematics
1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
1 Functional Analysis and its Applications
1 Publications Mathématiques
1 International Journal of Circuit Theory and Applications
1 Journal of Computer and System Sciences
1 Mathematics and Computers in Simulation
1 Michigan Mathematical Journal
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Applied Mathematics and Mechanics. (English Edition)
1 Journal of Complexity
1 Computers & Operations Research
1 Dynamics and Stability of Systems
1 Neural Networks
1 European Journal of Applied Mathematics
1 Annals of Physics
1 Linear Algebra and its Applications
1 Stochastic Processes and their Applications
1 Bulletin of the American Mathematical Society. New Series
1 Acta Mathematica Sinica. New Series
1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
1 Journal of Computer and Systems Sciences International
1 Journal of Mathematical Sciences (New York)
1 NoDEA. Nonlinear Differential Equations and Applications
1 Electronic Research Announcements of the American Mathematical Society
1 Bernoulli
1 Mathematical Problems in Engineering
1 Abstract and Applied Analysis
1 Discrete Dynamics in Nature and Society
1 Journal of Dynamical and Control Systems
1 Qualitative Theory of Dynamical Systems
1 International Journal of Nonlinear Sciences and Numerical Simulation
1 Physical Review Letters
1 Differential Equations
1 Nonlinear Analysis. Real World Applications
...and 9 more Serials
all top 5

Cited in 37 Fields

300 Dynamical systems and ergodic theory (37-XX)
124 Ordinary differential equations (34-XX)
53 Biology and other natural sciences (92-XX)
29 Mechanics of particles and systems (70-XX)
18 Probability theory and stochastic processes (60-XX)
18 Statistical mechanics, structure of matter (82-XX)
17 Partial differential equations (35-XX)
14 Measure and integration (28-XX)
13 Computer science (68-XX)
13 Information and communication theory, circuits (94-XX)
12 Difference and functional equations (39-XX)
12 Fluid mechanics (76-XX)
12 Systems theory; control (93-XX)
10 Numerical analysis (65-XX)
10 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
7 Combinatorics (05-XX)
7 General topology (54-XX)
6 Real functions (26-XX)
5 Global analysis, analysis on manifolds (58-XX)
5 Optics, electromagnetic theory (78-XX)
5 Operations research, mathematical programming (90-XX)
4 Number theory (11-XX)
4 Quantum theory (81-XX)
3 History and biography (01-XX)
3 Manifolds and cell complexes (57-XX)
3 Mechanics of deformable solids (74-XX)
2 Functions of a complex variable (30-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Operator theory (47-XX)
2 Statistics (62-XX)
2 Classical thermodynamics, heat transfer (80-XX)
1 Algebraic geometry (14-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Special functions (33-XX)
1 Integral equations (45-XX)
1 Functional analysis (46-XX)
1 Geometry (51-XX)

Citations by Year

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