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 Documents Indexed: 38 Publications since 1989
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Co-Authors

 8 single-authored 16 Holden, Arun V. 5 Biktasheva, I. V. 3 Brindley, John 3 Elkin, Yu. E. 3 Nikolaev, Eugene V. 3 Simitev, Radostin D. 3 Suckley, Rebecca 3 Tsyganov, Mikhail A. 2 Bezekci, Burhan 2 Zhang, Henggui 1 Afendikov, Andrei L. 1 Antonovsky, M. Ya. 1 Aponina, E. A. 1 Aptekarev, Alexander Ivanovich 1 Ataullakhanov, Fazoil I. 1 Balabaev, N. K. 1 Borisyuk, Roman M. 1 Bridge, Lloyd J. 1 Dagkesamanskii, R. D. 1 Dawes, William N. 1 Haken, Hermann 1 Ilyashenko, Yulij Sergeevich 1 Khibnik, Alexander I. 1 Krinsky, Valentin I. 1 Kuznetsov, Yuri Alexandrovich 1 Lakhno, Victor D. 1 Lunin, V. Yu. 1 Lunina, N. L. 1 Mironov, S. F. 1 Paszek, Pawel 1 Pertsov, Arkady M. 1 Posvyanskii, Vladimir S. 1 Roitberg, M. A. 1 Ryaben’kiĭ, Viktor Solomonovich 1 Ryashko, Lev Borisovich 1 Saumarez, R. C. 1 Savill, A. Mark 1 Sinaĭ, Yakov Grigor’evich 1 Starý, Tomáš 1 Tikhomirov, Vladimir Mikhaĭlovich 1 Tokarev, A. A. 1 Urzhumtsev, Alexandre G. 1 Vvedenskaya, Nikita Dmitrievna 1 West, Simon 1 White, Michael R. H. 1 Zaĭtsev, Alekseĭ Vyacheslavovich 1 Zarkhin, Yuriĭ Gennad’evich
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Serials

 11 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Chaos 4 Chaos, Solitons and Fractals 4 Physica D 3 Journal of Mathematical Biology 3 Bulletin of Mathematical Biology 1 Russian Mathematical Surveys 1 Philosophical Transactions of the Royal Society of London. Series A 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Nonlinear Mathematical Physics 1 Cubo Matemática Educacional
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Fields

 29 Biology and other natural sciences (92-XX) 20 Partial differential equations (35-XX) 10 Dynamical systems and ergodic theory (37-XX) 4 Fluid mechanics (76-XX) 3 Ordinary differential equations (34-XX) 3 Numerical analysis (65-XX) 1 History and biography (01-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX)

Citations contained in zbMATH Open

33 Publications have been cited 235 times in 168 Documents Cited by Year
Tension of organizing filaments of scroll waves. Zbl 0862.92002
Biktashev, V. N.; Holden, A. V.; Zhang, H.
1994
Resonant drift of autowave vortices in two dimensions and the effects of boundaries and inhomogeneities. Zbl 0925.92022
Biktashev, V. N.; Holden, A. V.
1995
A cross-diffusion model of forest boundary dynamics. Zbl 0790.92028
Kuznetsov, Yu. A.; Antonovsky, M. Ya.; Biktashev, V. N.; Aponina, E.
1994
Reentrant waves and their elimination in a model of mammalian ventricular tissue. Zbl 1069.92501
Biktashev, V. N.; Holden, A. V.
1998
Pursuit-evasion predator-prey waves in two spatial dimensions. Zbl 1080.35036
Biktashev, V. N.; Brindley, J.; Holden, A. V.; Tsyganov, M. A.
2004
Spiral wave meander and symmetry of the plane. Zbl 1298.35008
Biktashev, V. N.; Holden, A. V.; Nikolaev, E. V.
1996
Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator–prey pursuit and evasion example. Zbl 1057.92057
Tsyganov, M. A.; Brindley, J.; Holden, A. V.; Biktashev, V. N.
2004
The asymptotic structure of the Hodgkin-Huxley equations. Virtual tissue engineering of the heart. Zbl 1057.37079
2003
On the movement of excitation wave breaks. Zbl 0939.92001
Elkin, Yu. E.; Biktashev, V. N.; Holden, A. V.
1998
Diffusion of autowaves. Evolution equation for slowly varying autowaves. Zbl 0683.76072
Biktashev, V. N.
1989
Deterministic Brownian motion in the hypermeander of spiral waves. Zbl 0922.58049
Biktashev, V. N.; Holden, A. V.
1998
Solitary waves in excitable systems with cross-diffusion. Zbl 1370.35174
Biktashev, Vadim N.; Tsyganov, Mikhail A.
2005
A simplified model of propagation and dissipation of excitation fronts. Virtual tissue engineering of the heart. Zbl 1061.92034
Biktashev, V. N.
2003
Localization of response functions of spiral waves in the FitzHugh-Nagumo system. Zbl 1145.35399
Biktasheva, I. V.; Holden, A. V.; Biktashev, V. N.
2006
Three-dimensional aspects of re-entry in experimental and numerical models of ventricular fibrillation. Zbl 0962.92019
Biktashev, V. N.; Holden, A. V.; Mironov, S. F.; Pertsov, A. M.; Zaitsev, A. V.
1999
A model for the action of external current onto excitable tissue. Zbl 0891.92008
Biktashev, V. N.; Holden, A. V.; Zhang, H.
1997
Asymptotics of conduction velocity restitution in models of electrical excitation in the heart. Zbl 1209.92004
Simitev, R. D.; Biktashev, V. N.
2011
A simple mathematical model of gradual Darwinian evolution: emergence of a Gaussian trait distribution in adaptation along a fitness gradient. Zbl 1288.35273
2014
Response functions of spiral wave solutions of the complex Ginzburg-Landau equation. Zbl 0976.35077
Biktasheva, I. V.; Biktashev, V. N.
2001
Computational biology of propagation in excitable media models of cardiac tissue. Zbl 1004.92013
Holden, A. V.; Biktashev, V. N.
2002
Asymptotic properties of mathematical models of excitability. Zbl 1152.37348
Biktasheva, I. V.; Simitev, R. D.; Suckley, R.; Biktashev, V. N.
2006
Evolution of twist of an autowave vortex. Zbl 0666.76117
Biktashev, V. N.
1989
Waves of constant shape and the structure of the “rotors boundary” in excitable media. Zbl 0997.35101
Elkin, Yu. E.; Biktashev, V. N.; Holden, A. V.
2002
Phytoplankton blooms and fish recruitment rate: effects of spatial distribution. Zbl 1334.92442
Biktashev, V. N.; Brindley, J.
2004
Asymptotic analysis and analytical solutions of a model of cardiac excitation. Zbl 1139.92006
Biktashev, V. N.; Suckley, R.; Elkin, Y. E.; Simitev, R. D.
2008
A three-dimensional autowave turbulence. Zbl 0973.76566
Biktashev, V. N.
1998
On bifurcations of spiral waves in the plane. Zbl 1192.35018
Nikolaev, E. V.; Biktashev, V. N.; Holden, A. V.
1999
A method of ‘speed coefficients’ for biochemical model reduction applied to the NF-$$\kappa$$B system. Zbl 1306.92022
West, Simon; Bridge, Lloyd J.; White, Michael R. H.; Paszek, Pawel; Biktashev, Vadim N.
2015
A wave approach to pattern recognition (with application to optical character recognition). Zbl 0872.68162
Biktashev, Vadim; Krinsky, Valentin; Haken, Hermann
1994
A three-dimensional autowave turbulence. Zbl 1109.35377
Biktashev, V. N.
1998
Dissipation of the excitation front as a mechanism of self-terminating arrhythmias. Virtual tissue engineering of the heart. Zbl 1058.92023
Biktasheva, I. V.; Biktashev, V. N.; Dawes, W. N.; Holden, A. V.; Saumarez, R. C.; Savill, A. M.
2003
Strength-duration relationship in an excitable medium. Zbl 1452.35058
Bezekci, Burhan; Biktashev, V. N.
2020
Fast-slow asymptotic for semi-analytical ignition criteria in Fitzhugh-Nagumo system. Zbl 1394.35024
Bezekci, B.; Biktashev, V. N.
2017
Strength-duration relationship in an excitable medium. Zbl 1452.35058
Bezekci, Burhan; Biktashev, V. N.
2020
Fast-slow asymptotic for semi-analytical ignition criteria in Fitzhugh-Nagumo system. Zbl 1394.35024
Bezekci, B.; Biktashev, V. N.
2017
A method of ‘speed coefficients’ for biochemical model reduction applied to the NF-$$\kappa$$B system. Zbl 1306.92022
West, Simon; Bridge, Lloyd J.; White, Michael R. H.; Paszek, Pawel; Biktashev, Vadim N.
2015
A simple mathematical model of gradual Darwinian evolution: emergence of a Gaussian trait distribution in adaptation along a fitness gradient. Zbl 1288.35273
2014
Asymptotics of conduction velocity restitution in models of electrical excitation in the heart. Zbl 1209.92004
Simitev, R. D.; Biktashev, V. N.
2011
Asymptotic analysis and analytical solutions of a model of cardiac excitation. Zbl 1139.92006
Biktashev, V. N.; Suckley, R.; Elkin, Y. E.; Simitev, R. D.
2008
Localization of response functions of spiral waves in the FitzHugh-Nagumo system. Zbl 1145.35399
Biktasheva, I. V.; Holden, A. V.; Biktashev, V. N.
2006
Asymptotic properties of mathematical models of excitability. Zbl 1152.37348
Biktasheva, I. V.; Simitev, R. D.; Suckley, R.; Biktashev, V. N.
2006
Solitary waves in excitable systems with cross-diffusion. Zbl 1370.35174
Biktashev, Vadim N.; Tsyganov, Mikhail A.
2005
Pursuit-evasion predator-prey waves in two spatial dimensions. Zbl 1080.35036
Biktashev, V. N.; Brindley, J.; Holden, A. V.; Tsyganov, M. A.
2004
Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator–prey pursuit and evasion example. Zbl 1057.92057
Tsyganov, M. A.; Brindley, J.; Holden, A. V.; Biktashev, V. N.
2004
Phytoplankton blooms and fish recruitment rate: effects of spatial distribution. Zbl 1334.92442
Biktashev, V. N.; Brindley, J.
2004
The asymptotic structure of the Hodgkin-Huxley equations. Virtual tissue engineering of the heart. Zbl 1057.37079
2003
A simplified model of propagation and dissipation of excitation fronts. Virtual tissue engineering of the heart. Zbl 1061.92034
Biktashev, V. N.
2003
Dissipation of the excitation front as a mechanism of self-terminating arrhythmias. Virtual tissue engineering of the heart. Zbl 1058.92023
Biktasheva, I. V.; Biktashev, V. N.; Dawes, W. N.; Holden, A. V.; Saumarez, R. C.; Savill, A. M.
2003
Computational biology of propagation in excitable media models of cardiac tissue. Zbl 1004.92013
Holden, A. V.; Biktashev, V. N.
2002
Waves of constant shape and the structure of the “rotors boundary” in excitable media. Zbl 0997.35101
Elkin, Yu. E.; Biktashev, V. N.; Holden, A. V.
2002
Response functions of spiral wave solutions of the complex Ginzburg-Landau equation. Zbl 0976.35077
Biktasheva, I. V.; Biktashev, V. N.
2001
Three-dimensional aspects of re-entry in experimental and numerical models of ventricular fibrillation. Zbl 0962.92019
Biktashev, V. N.; Holden, A. V.; Mironov, S. F.; Pertsov, A. M.; Zaitsev, A. V.
1999
On bifurcations of spiral waves in the plane. Zbl 1192.35018
Nikolaev, E. V.; Biktashev, V. N.; Holden, A. V.
1999
Reentrant waves and their elimination in a model of mammalian ventricular tissue. Zbl 1069.92501
Biktashev, V. N.; Holden, A. V.
1998
On the movement of excitation wave breaks. Zbl 0939.92001
Elkin, Yu. E.; Biktashev, V. N.; Holden, A. V.
1998
Deterministic Brownian motion in the hypermeander of spiral waves. Zbl 0922.58049
Biktashev, V. N.; Holden, A. V.
1998
A three-dimensional autowave turbulence. Zbl 0973.76566
Biktashev, V. N.
1998
A three-dimensional autowave turbulence. Zbl 1109.35377
Biktashev, V. N.
1998
A model for the action of external current onto excitable tissue. Zbl 0891.92008
Biktashev, V. N.; Holden, A. V.; Zhang, H.
1997
Spiral wave meander and symmetry of the plane. Zbl 1298.35008
Biktashev, V. N.; Holden, A. V.; Nikolaev, E. V.
1996
Resonant drift of autowave vortices in two dimensions and the effects of boundaries and inhomogeneities. Zbl 0925.92022
Biktashev, V. N.; Holden, A. V.
1995
Tension of organizing filaments of scroll waves. Zbl 0862.92002
Biktashev, V. N.; Holden, A. V.; Zhang, H.
1994
A cross-diffusion model of forest boundary dynamics. Zbl 0790.92028
Kuznetsov, Yu. A.; Antonovsky, M. Ya.; Biktashev, V. N.; Aponina, E.
1994
A wave approach to pattern recognition (with application to optical character recognition). Zbl 0872.68162
Biktashev, Vadim; Krinsky, Valentin; Haken, Hermann
1994
Diffusion of autowaves. Evolution equation for slowly varying autowaves. Zbl 0683.76072
Biktashev, V. N.
1989
Evolution of twist of an autowave vortex. Zbl 0666.76117
Biktashev, V. N.
1989
all top 5

Cited by 297 Authors

 24 Biktashev, Vadim N. 21 Holden, Arun V. 8 Panfilov, Alexander V. 6 Ramos, Juan I. 5 Dierckx, Hans 5 Rao, Feng 4 Alfaro, Matthieu 4 Pravdin, Sergei F. 3 Alonso, Sergio 3 Biktasheva, I. V. 3 Clayton, Richard H. 3 Jalife, José 3 Lin, Yuanqu 3 Melbourne, Ian 3 Pertsov, Arkady M. 3 Tsyganov, Mikhail A. 3 Wang, Weiming 3 Winfree, Arthur Taylor 3 Wu, Yaping 3 Yagi, Atsushi 3 Zhang, Henggui 2 Anishchenko, Vadim Semenovich 2 Banerjee, Malay 2 Benson, Alan P. 2 Berenfeld, Omer 2 Berezovskaya, Faina Semenovna 2 Bezekci, Burhan 2 Bhattacharyya, Rakhi 2 Carles, Rémi 2 Cherry, Elizabeth M. 2 Dong, Xunde 2 Elkin, Yu. E. 2 Fenton, Flavio H. 2 Jin, Zhen 2 Kang, Yun 2 Karma, Alain 2 Keener, James P. 2 Krause, Andrew L. 2 Kuklik, Paweł 2 Kwiatkowska, Marta Z. 2 Li, Bing-Wei 2 Li, Pan 2 Lian, Xinze 2 Lin, Yezhi 2 Mukherjee, Nayana 2 Mukhopadhyay, Banibrata 2 Sáiz, Javier 2 Shepelev, Igor’ Aleksandrovich 2 Simitev, Radostin D. 2 Solonnikov, Vsevolod Alekseevich 2 Suckley, Rebecca 2 van Gorder, Robert Ashton 2 Veruete, Mario 2 Vinson, Michael J. 2 Wang, Cong 2 Wang, Hailing 2 Żebrowski, Jan Jacek 1 Abdelmalek, Salem 1 Alueva, Yuliya S. 1 Arditi, Roger 1 Arens, Sander 1 Ashwin, Peter 1 Aslanidi, Oleg V. 1 Baglama, James 1 Bär, Markus 1 Baranowski, Rafal 1 Baricz, Árpád 1 Barkley, Dwight 1 Bendoukha, Samir 1 Bernoff, Andrew J. 1 Bernus, O. 1 Beyn, Wolf-Jürgen 1 Bini, Donato 1 Bobisud, Larry E. 1 Bogar, K. 1 Bridge, Lloyd J. 1 Brindley, John 1 Buchner, Teodor 1 Budzinskiy, Stanislav S. 1 Bukh, Andrei V. 1 Cai, Yongli 1 Cantin, Guillaume 1 Castillo-Chavez, Carlos 1 Che, Yanqiu 1 Chen, Liping 1 Chen, Nan 1 Cherubini, Christian 1 Chuan, Le Huy 1 Chumarnaya, Tatyana V. 1 Clegg, Gareth 1 Clewley, Robert 1 Cvitanović, Predrag 1 Dai, Feng 1 Dawes, William N. 1 de la Casa, Miguel A. 1 de la Rubia, F. Javier 1 d’Onofrio, Alberto 1 Dubey, Balram 1 Ellison, Rebecca 1 Epanchintsev, Timofei I. ...and 197 more Authors
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Cited in 61 Serials

 26 Chaos 23 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 14 Chaos, Solitons and Fractals 12 Physica D 7 Bulletin of Mathematical Biology 6 Journal of Mathematical Analysis and Applications 6 Communications in Nonlinear Science and Numerical Simulation 4 Mathematical Biosciences 4 Applied Mathematics and Computation 4 Discrete Dynamics in Nature and Society 3 Russian Journal of Numerical Analysis and Mathematical Modelling 3 Nonlinear Analysis. Real World Applications 3 Journal of Theoretical Biology 2 Mathematics and Computers in Simulation 2 Mathematical Problems in Engineering 2 Mathematical Modelling of Natural Phenomena 2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 International Journal of Modern Physics B 1 Journal of Computational Physics 1 Journal of the Franklin Institute 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Wave Motion 1 Glasgow Mathematical Journal 1 International Journal of Circuit Theory and Applications 1 Journal of Differential Equations 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Proceedings of the American Mathematical Society 1 Ricerche di Matematica 1 Theoretical Computer Science 1 Chinese Annals of Mathematics. Series B 1 Science in China. Series A 1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 1 International Journal of Adaptive Control and Signal Processing 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Computational Mathematics and Mathematical Physics 1 Applied Mathematical Modelling 1 Proceedings of the National Academy of Sciences of the United States of America 1 Expositiones Mathematicae 1 Chinese Science Bulletin 1 Journal of Dynamics and Differential Equations 1 Journal of Nonlinear Science 1 Journal of Computational Neuroscience 1 Nonlinear Dynamics 1 Abstract and Applied Analysis 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 New Journal of Physics 1 Regular and Chaotic Dynamics 1 Journal of Biological Systems 1 Journal of Nonlinear Mathematical Physics 1 Discrete and Continuous Dynamical Systems. Series B 1 Physical Review E. Third Series 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Advances in Complex Systems 1 Communications on Pure and Applied Analysis 1 Journal of Statistical Mechanics: Theory and Experiment 1 Mathematical Biosciences and Engineering 1 Journal of Physics A: Mathematical and Theoretical 1 International Journal of Biomathematics 1 Statistics and Computing 1 Nonlinear Analysis. Theory, Methods & Applications
all top 5

Cited in 21 Fields

 115 Biology and other natural sciences (92-XX) 74 Partial differential equations (35-XX) 37 Dynamical systems and ergodic theory (37-XX) 20 Ordinary differential equations (34-XX) 11 Numerical analysis (65-XX) 8 Fluid mechanics (76-XX) 7 Computer science (68-XX) 5 Probability theory and stochastic processes (60-XX) 4 Operator theory (47-XX) 3 Integral equations (45-XX) 3 Statistics (62-XX) 3 Optics, electromagnetic theory (78-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Special functions (33-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Difference and functional equations (39-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Information and communication theory, circuits (94-XX)