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## Mirollo, Renato E.

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 Author ID: mirollo.renato-e Published as: Mirollo, R.; Mirollo, R. E.; Mirollo, Renato; Mirollo, Renato E.; Mirollo, Rennie
 Documents Indexed: 20 Publications since 1987
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#### Co-Authors

 2 single-authored 13 Strogatz, Steven Henry 3 Engelbrecht, Jan R. 2 Chen, Bolun 2 Matthews, Paul Charles 1 Marcus, Charles M. 1 Marvel, Seth A. 1 Rosen, Ned 1 Tsang, Kwok Yeung 1 Vilonen, Kari 1 Westervelt, Robert M. 1 Wiesenfeld, Kurt
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#### Serials

 5 Physica D 4 Chaos 3 SIAM Journal on Applied Mathematics 1 American Mathematical Monthly 1 Journal of Statistical Physics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Journal of Physics A: Mathematical and General 1 SIAM Journal on Mathematical Analysis 1 Journal of Nonlinear Science 1 Physical Review Letters 1 Journal of Physics A: Mathematical and Theoretical
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#### Fields

 13 Ordinary differential equations (34-XX) 7 Dynamical systems and ergodic theory (37-XX) 5 Statistical mechanics, structure of matter (82-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of particles and systems (70-XX) 2 Biology and other natural sciences (92-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Category theory; homological algebra (18-XX) 1 Real functions (26-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Partial differential equations (35-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

20 Publications have been cited 722 times in 560 Documents Cited by Year
Synchronization of pulse-coupled biological oscillators. Zbl 0712.92006
Mirollo, Renato E.; Strogatz, Steven H.
1990
The spectrum of the locked state for the Kuramoto model of coupled oscillators. Zbl 1085.34033
Mirollo, Renato E.; Strogatz, Steven H.
2005
The spectrum of the partially locked state for the Kuramoto model. Zbl 1119.37051
Mirollo, R.; Strogatz, S. H.
2007
Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping. Zbl 0969.92501
Strogatz, Steven H.; Mirollo, Renato E.; Matthews, Paul C.
1992
Amplitude death in an array of limit-cycle oscillators. Zbl 1086.34525
Mirollo, Renato E.; Strogatz, Steven H.
1990
Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action. Zbl 1311.34082
Marvel, Seth A.; Mirollo, Renato E.; Strogatz, Steven H.
2009
Dynamics of a large system of coupled nonlinear oscillators. Zbl 0742.34035
Matthews, Paul C.; Mirollo, Renato E.; Strogatz, Steven H.
1991
Dynamics of a globally coupled oscillator array. Zbl 0718.34060
Tsang, Kwok Yeung; Mirollo, Renato E.; Strogatz, Steven H.; Wiesenfeld, Kurt
1991
Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies. Zbl 0642.60047
Strogatz, Steven H.; Mirollo, Renato E.
1988
Collective synchronisation in lattices of non-linear oscillators with randomness. Zbl 0654.60105
Strogatz, Steven H.; Mirollo, Renato E.
1988
Bernstein-Gelfand-Gelfand reciprocity on perverse sheaves. Zbl 0651.14010
Mirollo, R.; Vilonen, K.
1987
The asymptotic behavior of the order parameter for the infinite-$$N$$ Kuramoto model. Zbl 1319.34059
Mirollo, Renato E.
2012
Splay-phase orbits for equivariant flows on tori. Zbl 0815.34036
Mirollo, Renato E.
1994
Collective dynamics of coupled oscillators with random pinning. Zbl 0672.70031
Strogatz, Steven H.; Marcus, Charles M.; Westervelt, Robert M.; Mirollo, Renato E.
1989
Hyperbolic geometry of Kuramoto oscillator networks. Zbl 1377.35248
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
2017
Classification of attractors for systems of identical coupled Kuramoto oscillators. Zbl 1374.34104
Engelbrecht, Jan R.; Mirollo, Renato
2014
Existence, uniqueness, and nonuniqueness of single-wave-form solutions to Josephson junction systems. Zbl 0958.34034
Mirollo, Rennie; Rosen, Ned
2000
Jump bifurcation and hysteresis in an infinite-dimensional dynamical system of coupled spins. Zbl 0692.58043
Mirollo, Renato E.; Strogatz, Steven H.
1990
Integral representation of a finite spike. Zbl 0776.26005
Mirollo, R. E.; Strogatz, S. H.
1990
Dynamics of the Kuramoto-Sakaguchi oscillator network with asymmetric order parameter. Zbl 1406.34063
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
2019
Dynamics of the Kuramoto-Sakaguchi oscillator network with asymmetric order parameter. Zbl 1406.34063
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
2019
Hyperbolic geometry of Kuramoto oscillator networks. Zbl 1377.35248
Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato
2017
Classification of attractors for systems of identical coupled Kuramoto oscillators. Zbl 1374.34104
Engelbrecht, Jan R.; Mirollo, Renato
2014
The asymptotic behavior of the order parameter for the infinite-$$N$$ Kuramoto model. Zbl 1319.34059
Mirollo, Renato E.
2012
Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action. Zbl 1311.34082
Marvel, Seth A.; Mirollo, Renato E.; Strogatz, Steven H.
2009
The spectrum of the partially locked state for the Kuramoto model. Zbl 1119.37051
Mirollo, R.; Strogatz, S. H.
2007
The spectrum of the locked state for the Kuramoto model of coupled oscillators. Zbl 1085.34033
Mirollo, Renato E.; Strogatz, Steven H.
2005
Existence, uniqueness, and nonuniqueness of single-wave-form solutions to Josephson junction systems. Zbl 0958.34034
Mirollo, Rennie; Rosen, Ned
2000
Splay-phase orbits for equivariant flows on tori. Zbl 0815.34036
Mirollo, Renato E.
1994
Coupled nonlinear oscillators below the synchronization threshold: Relaxation by generalized Landau damping. Zbl 0969.92501
Strogatz, Steven H.; Mirollo, Renato E.; Matthews, Paul C.
1992
Dynamics of a large system of coupled nonlinear oscillators. Zbl 0742.34035
Matthews, Paul C.; Mirollo, Renato E.; Strogatz, Steven H.
1991
Dynamics of a globally coupled oscillator array. Zbl 0718.34060
Tsang, Kwok Yeung; Mirollo, Renato E.; Strogatz, Steven H.; Wiesenfeld, Kurt
1991
Synchronization of pulse-coupled biological oscillators. Zbl 0712.92006
Mirollo, Renato E.; Strogatz, Steven H.
1990
Amplitude death in an array of limit-cycle oscillators. Zbl 1086.34525
Mirollo, Renato E.; Strogatz, Steven H.
1990
Jump bifurcation and hysteresis in an infinite-dimensional dynamical system of coupled spins. Zbl 0692.58043
Mirollo, Renato E.; Strogatz, Steven H.
1990
Integral representation of a finite spike. Zbl 0776.26005
Mirollo, R. E.; Strogatz, S. H.
1990
Collective dynamics of coupled oscillators with random pinning. Zbl 0672.70031
Strogatz, Steven H.; Marcus, Charles M.; Westervelt, Robert M.; Mirollo, Renato E.
1989
Phase-locking and critical phenomena in lattices of coupled nonlinear oscillators with random intrinsic frequencies. Zbl 0642.60047
Strogatz, Steven H.; Mirollo, Renato E.
1988
Collective synchronisation in lattices of non-linear oscillators with randomness. Zbl 0654.60105
Strogatz, Steven H.; Mirollo, Renato E.
1988
Bernstein-Gelfand-Gelfand reciprocity on perverse sheaves. Zbl 0651.14010
Mirollo, R.; Vilonen, K.
1987
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#### Cited by 987 Authors

 38 Ha, Seung-Yeal 10 Pikovsky, Arkady S. 9 Chen, Tianping 9 Kurths, Jürgen 9 Strogatz, Steven Henry 8 Ott, Edward 7 Jaćimović, Vladimir 7 Laing, Carlo R. 7 Mirollo, Renato E. 7 Qin, Wenxin 7 Rosenblum, Michael G. 6 Antonsen, Thomas M. jun. 6 Bonilla, Luis Lopez 6 Bronski, Jared C. 6 Catsigeras, Eleonora 6 Choi, Young-Pil 6 DeVille, Lee 6 Fernandez, Bastien 6 Li, Zhuchun 6 Lu, Wenlian 6 Park, Jinyeong 5 Aihara, Kazuyuki 5 Chiu, Chuang-Hsiung 5 Coombes, Stephen 5 Crnkić, Aladin 5 Lohé, M. A. 5 Park, Hansol 5 Ryoo, Sang Woo 5 Timme, Marc 5 Zou, Wei 4 Akhmet, Marat Ubaydulla 4 Bick, Christian 4 Bullo, Francesco 4 Canavier, Carmen C. 4 Chiba, Hayato 4 Delabays, Robin 4 Deng, Bin 4 Ermentrout, Bard G. 4 Gottwald, Georg A. 4 Kim, Dohyun 4 Kim, Yongduck 4 Kopell, Nancy J. 4 Lee, Jaeseung 4 Li, Chun-Hsien 4 Lin, Wen-Wei 4 Noh, Se Eun 4 Ramírez Ávila, Gonzalo Marcelo 4 Shim, Woojoo 4 Skardal, Per Sebastian 4 Wang, Jiang 4 Yanchuk, Sergiĭ Volodymyrovych 4 Young, Lai-Sang 3 Ashwin, Peter 3 Barreto, Ernest 3 Belykh, Vladimir N. 3 Boccaletti, Stefano 3 Borisyuk, Roman M. 3 Burylko, Oleksandr 3 Deneubourg, Jean-Louis 3 Dörfler, Florian 3 Ermentrout, George Bard 3 Fei, Xiangyang 3 Geisel, Theo 3 Girvan, Michelle 3 Hasler, Martin J. 3 Hu, Cheng 3 Jacquod, Philippe 3 Jiang, Haijun 3 Kanamaru, Takashi 3 Kapitaniak, Tomasz 3 Kazanovich, Yakov B. 3 Ko, Dongnam 3 Konishi, Keiji 3 Li, Kezan 3 Liu, Xiwei 3 Nijmeijer, Henk 3 Omel’chenko, Oleh E. 3 Osipov, Grigory V. 3 Peng, Chenchang 3 Schöll, Eckehard 3 Sen, Abhijit 3 Shabunin, Alexey 3 So, Paul 3 Spigler, Renato 3 Swift, James W. 3 Volkov, Evgenij I. 3 Wang, Yongqiang 3 Wiesenfeld, Kurt 3 Wolfrum, Matthias 3 Yang, Junzhong 3 Yang, Suh-Yuh 3 Zhan, Meng 3 Zhang, Yinglong 3 Zhong, Shou-Ming 2 Acebrón, Juan A. 2 Achuthan, Srisairam 2 Almendral, Juan Antonio 2 Anishchenko, Vadim Semenovich 2 Aronson, Donald G. 2 Astakhov, Vladimir V. ...and 887 more Authors
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#### Cited in 115 Serials

 116 Chaos 68 Physica D 31 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 22 Journal of Statistical Physics 21 Neural Computation 16 Nonlinear Dynamics 15 Chaos, Solitons and Fractals 14 Communications in Nonlinear Science and Numerical Simulation 14 SIAM Journal on Applied Dynamical Systems 9 Journal of Nonlinear Science 8 Biological Cybernetics 7 Journal of Mathematical Physics 7 Journal of Computational Neuroscience 6 Journal of the Franklin Institute 6 Journal of Mathematical Biology 6 Journal of Differential Equations 6 Mathematical Problems in Engineering 6 Networks and Heterogeneous Media 6 The Journal of Mathematical Neuroscience 5 Physics Letters. A 5 Physics Reports 5 Bulletin of Mathematical Biology 5 Automatica 5 New Journal of Physics 4 Journal of Mathematical Analysis and Applications 4 Applied Mathematics and Computation 4 SIAM Journal on Applied Mathematics 4 Regular and Chaotic Dynamics 4 International Journal of Modern Physics C 4 Journal of Theoretical Biology 3 Nonlinearity 3 Quarterly of Applied Mathematics 3 Neural Networks 3 Discrete and Continuous Dynamical Systems 3 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Physical Review Letters 3 Journal of Statistical Mechanics: Theory and Experiment 2 Communications in Mathematical Physics 2 International Journal of Control 2 Transport Theory and Statistical Physics 2 Advances in Mathematics 2 Journal of Algebra 2 SIAM Journal on Control and Optimization 2 Transactions of the American Mathematical Society 2 Systems & Control Letters 2 Chinese Annals of Mathematics. Series B 2 Journal of Global Optimization 2 Automation and Remote Control 2 SIAM Journal on Mathematical Analysis 2 Journal of Dynamics and Differential Equations 2 Discrete Dynamics in Nature and Society 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Nonlinear Analysis. Real World Applications 2 Analysis and Applications (Singapore) 2 The European Physical Journal B. Condensed Matter and Complex Systems 2 Nonlinear Analysis. Hybrid Systems 2 Kinetic and Related Models 2 Nonlinear Analysis. Theory, Methods & Applications 1 International Journal of Modern Physics B 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 International Journal of Systems Science 1 Journal of Fluid Mechanics 1 Mathematical Biosciences 1 Physica A 1 Reports on Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Journal of Geometry and Physics 1 Compositio Mathematica 1 Functional Analysis and its Applications 1 Publications Mathématiques 1 International Journal of Circuit Theory and Applications 1 International Journal for Numerical Methods in Engineering 1 Mathematics and Computers in Simulation 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Ricerche di Matematica 1 SIAM Journal on Computing 1 Theoretical Computer Science 1 European Journal of Combinatorics 1 Ergodic Theory and Dynamical Systems 1 Acta Applicandae Mathematicae 1 Journal of Economic Dynamics & Control 1 Journal of the American Mathematical Society 1 Mathematical and Computer Modelling 1 European Journal of Applied Mathematics 1 Applied Mathematical Modelling 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Proceedings of the National Academy of Sciences of the United States of America 1 Bulletin of the American Mathematical Society. New Series 1 Formal Methods in System Design 1 Journal of Mathematical Sciences (New York) 1 Kyushu Journal of Mathematics 1 Science in China. Series E 1 Differential Equations and Dynamical Systems 1 Abstract and Applied Analysis 1 Journal of Shanghai University 1 PAA. Pattern Analysis and Applications 1 Journal of the European Mathematical Society (JEMS) 1 Annales Henri Poincaré 1 Dynamical Systems ...and 15 more Serials
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#### Cited in 41 Fields

 329 Ordinary differential equations (34-XX) 179 Biology and other natural sciences (92-XX) 140 Dynamical systems and ergodic theory (37-XX) 73 Systems theory; control (93-XX) 56 Statistical mechanics, structure of matter (82-XX) 44 Partial differential equations (35-XX) 29 Mechanics of particles and systems (70-XX) 23 Combinatorics (05-XX) 23 Information and communication theory, circuits (94-XX) 22 Computer science (68-XX) 16 Operations research, mathematical programming (90-XX) 10 Probability theory and stochastic processes (60-XX) 9 Numerical analysis (65-XX) 8 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Algebraic geometry (14-XX) 7 Difference and functional equations (39-XX) 6 Fluid mechanics (76-XX) 6 Optics, electromagnetic theory (78-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Associative rings and algebras (16-XX) 4 Integral equations (45-XX) 4 Operator theory (47-XX) 4 Quantum theory (81-XX) 3 Nonassociative rings and algebras (17-XX) 3 Category theory; homological algebra (18-XX) 3 Topological groups, Lie groups (22-XX) 3 Mechanics of deformable solids (74-XX) 2 Commutative algebra (13-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Functional analysis (46-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX)