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Route to chaotic synchronisation in coupled map lattices: Rigorous results
Non-smooth pitchfork bifurcations
1. | Department of Mathematics, UMIST, P.O. Box 88, Manchester M60 1QD, United Kingdom |
[1] |
Saša Kocić, João Lopes Dias. Reducibility of quasi-periodically forced circle flows. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5325-5345. doi: 10.3934/dcds.2020229 |
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Àngel Jorba, Pau Rabassa, Joan Carles Tatjer. Period doubling and reducibility in the quasi-periodically forced logistic map. Discrete and Continuous Dynamical Systems - B, 2012, 17 (5) : 1507-1535. doi: 10.3934/dcdsb.2012.17.1507 |
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Lufang Mi, Kangkang Zhang. Invariant Tori for Benjamin-Ono Equation with Unbounded quasi-periodically forced Perturbation. Discrete and Continuous Dynamical Systems, 2014, 34 (2) : 689-707. doi: 10.3934/dcds.2014.34.689 |
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Àngel Jorba, Joan Carles Tatjer. A mechanism for the fractalization of invariant curves in quasi-periodically forced 1-D maps. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 537-567. doi: 10.3934/dcdsb.2008.10.537 |
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Michal Fečkan. Bifurcation from degenerate homoclinics in periodically forced systems. Discrete and Continuous Dynamical Systems, 1999, 5 (2) : 359-374. doi: 10.3934/dcds.1999.5.359 |
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Jie Liu, Jianguo Si. Invariant tori of a nonlinear Schrödinger equation with quasi-periodically unbounded perturbations. Communications on Pure and Applied Analysis, 2017, 16 (1) : 25-68. doi: 10.3934/cpaa.2017002 |
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Yangjian Sun, Changjian Liu. The Poincaré bifurcation of a SD oscillator. Discrete and Continuous Dynamical Systems - B, 2021, 26 (3) : 1565-1577. doi: 10.3934/dcdsb.2020173 |
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Alexandre Rodrigues. "Large" strange attractors in the unfolding of a heteroclinic attractor. Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2355-2379. doi: 10.3934/dcds.2021193 |
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Runxia Wang, Haihong Liu, Fang Yan, Xiaohui Wang. Hopf-pitchfork bifurcation analysis in a coupled FHN neurons model with delay. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 523-542. doi: 10.3934/dcdss.2017026 |
[10] |
Shengqing Hu. Persistence of invariant tori for almost periodically forced reversible systems. Discrete and Continuous Dynamical Systems, 2020, 40 (7) : 4497-4518. doi: 10.3934/dcds.2020188 |
[11] |
Alain Léger, Elaine Pratt. On the equilibria and qualitative dynamics of a forced nonlinear oscillator with contact and friction. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 501-527. doi: 10.3934/dcdss.2016009 |
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Shengfu Deng. Generalized pitchfork bifurcation on a two-dimensional gaseous star with self-gravity and surface tension. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3419-3435. doi: 10.3934/dcds.2014.34.3419 |
[13] |
John E. Franke, Abdul-Aziz Yakubu. Periodically forced discrete-time SIS epidemic model with disease induced mortality. Mathematical Biosciences & Engineering, 2011, 8 (2) : 385-408. doi: 10.3934/mbe.2011.8.385 |
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Olivier Goubet, Ezzeddine Zahrouni. Global attractor for damped forced nonlinear logarithmic Schrödinger equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2933-2946. doi: 10.3934/dcdss.2020393 |
[15] |
Leonid A. Bunimovich. Chaotic and nonchaotic mushrooms. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 63-74. doi: 10.3934/dcds.2008.22.63 |
[16] |
Andrew Comech. Weak attractor of the Klein-Gordon field in discrete space-time interacting with a nonlinear oscillator. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2711-2755. doi: 10.3934/dcds.2013.33.2711 |
[17] |
Lei Jiao, Yiqian Wang. The construction of quasi-periodic solutions of quasi-periodic forced Schrödinger equation. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1585-1606. doi: 10.3934/cpaa.2009.8.1585 |
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Boling Guo, Zhaohui Huo. The global attractor of the damped, forced generalized Korteweg de Vries-Benjamin-Ono equation in $L^2$. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 121-136. doi: 10.3934/dcds.2006.16.121 |
[19] |
Kotaro Tsugawa. Existence of the global attractor for weakly damped, forced KdV equation on Sobolev spaces of negative index. Communications on Pure and Applied Analysis, 2004, 3 (2) : 301-318. doi: 10.3934/cpaa.2004.3.301 |
[20] |
Moncef Aouadi, Alain Miranville. Quasi-stability and global attractor in nonlinear thermoelastic diffusion plate with memory. Evolution Equations and Control Theory, 2015, 4 (3) : 241-263. doi: 10.3934/eect.2015.4.241 |
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