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Random attractorsgeneral properties, existence and applications to stochastic bifurcation theory
1.  Department of Economics, University of Bielefeld, P.O.Box 100 131, 33501 Bielefeld, Germany 
[1] 
Zhaosheng Feng. Duffingvan der Poltype oscillator systems. Discrete & Continuous Dynamical Systems  S, 2014, 7 (6) : 12311257. doi: 10.3934/dcdss.2014.7.1231 
[2] 
Stefan Siegmund. Normal form of Duffingvan der Pol oscillator under nonautonomous parametric perturbations. Conference Publications, 2001, 2001 (Special) : 357361. doi: 10.3934/proc.2001.2001.357 
[3] 
Bixiang Wang. Random attractors for nonautonomous stochastic wave equations with multiplicative noise. Discrete & Continuous Dynamical Systems  A, 2014, 34 (1) : 269300. doi: 10.3934/dcds.2014.34.269 
[4] 
Xiaojun Li, Xiliang Li, Kening Lu. Random attractors for stochastic parabolic equations with additive noise in weighted spaces. Communications on Pure & Applied Analysis, 2018, 17 (3) : 729749. doi: 10.3934/cpaa.2018038 
[5] 
Ludwig Arnold, Igor Chueshov. Cooperative random and stochastic differential equations. Discrete & Continuous Dynamical Systems  A, 2001, 7 (1) : 133. doi: 10.3934/dcds.2001.7.1 
[6] 
Fuke Wu, Peter E. Kloeden. Meansquare random attractors of stochastic delay differential equations with random delay. Discrete & Continuous Dynamical Systems  B, 2013, 18 (6) : 17151734. doi: 10.3934/dcdsb.2013.18.1715 
[7] 
María J. Garrido–Atienza, Kening Lu, Björn Schmalfuss. Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 473493. doi: 10.3934/dcdsb.2010.14.473 
[8] 
Björn Schmalfuss. Attractors for nonautonomous and random dynamical systems perturbed by impulses. Discrete & Continuous Dynamical Systems  A, 2003, 9 (3) : 727744. doi: 10.3934/dcds.2003.9.727 
[9] 
Boris Anicet Guimfack, Conrad Bertrand Tabi, Alidou Mohamadou, Timoléon Crépin Kofané. Stochastic dynamics of the FitzHughNagumo neuron model through a modified Van der Pol equation with fractionalorder term and Gaussian white noise excitation. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020397 
[10] 
Wenqiang Zhao. Pullback attractors for bispatial continuous random dynamical systems and application to stochastic fractional power dissipative equation on an unbounded domain. Discrete & Continuous Dynamical Systems  B, 2019, 24 (7) : 33953438. doi: 10.3934/dcdsb.2018326 
[11] 
Abiti Adili, Bixiang Wang. Random attractors for nonautonomous stochastic FitzHughNagumo systems with multiplicative noise. Conference Publications, 2013, 2013 (special) : 110. doi: 10.3934/proc.2013.2013.1 
[12] 
Zhaojuan Wang, Shengfan Zhou. Existence and upper semicontinuity of random attractors for nonautonomous stochastic strongly damped wave equation with multiplicative noise. Discrete & Continuous Dynamical Systems  A, 2017, 37 (5) : 27872812. doi: 10.3934/dcds.2017120 
[13] 
Lianfa He, Hongwen Zheng, Yujun Zhu. Shadowing in random dynamical systems. Discrete & Continuous Dynamical Systems  A, 2005, 12 (2) : 355362. doi: 10.3934/dcds.2005.12.355 
[14] 
Philippe Marie, Jérôme Rousseau. Recurrence for random dynamical systems. Discrete & Continuous Dynamical Systems  A, 2011, 30 (1) : 116. doi: 10.3934/dcds.2011.30.1 
[15] 
Zhaosheng Feng, Guangyue Gao, Jing Cui. Duffingvan der Poltype oscillator system and its first integrals. Communications on Pure & Applied Analysis, 2011, 10 (5) : 13771391. doi: 10.3934/cpaa.2011.10.1377 
[16] 
Tomás Caraballo, José A. Langa, James C. Robinson. Stability and random attractors for a reactiondiffusion equation with multiplicative noise. Discrete & Continuous Dynamical Systems  A, 2000, 6 (4) : 875892. doi: 10.3934/dcds.2000.6.875 
[17] 
Chi Phan. Random attractor for stochastic HindmarshRose equations with multiplicative noise. Discrete & Continuous Dynamical Systems  B, 2020, 25 (8) : 32333256. doi: 10.3934/dcdsb.2020060 
[18] 
Tomás Caraballo, Stefanie Sonner. Random pullback exponential attractors: General existence results for random dynamical systems in Banach spaces. Discrete & Continuous Dynamical Systems  A, 2017, 37 (12) : 63836403. doi: 10.3934/dcds.2017277 
[19] 
Markus Böhm, Björn Schmalfuss. Bounds on the Hausdorff dimension of random attractors for infinitedimensional random dynamical systems on fractals. Discrete & Continuous Dynamical Systems  B, 2019, 24 (7) : 31153138. doi: 10.3934/dcdsb.2018303 
[20] 
Jun Shen, Kening Lu, Bixiang Wang. Invariant manifolds and foliations for random differential equations driven by colored noise. Discrete & Continuous Dynamical Systems  A, 2020, 40 (11) : 62016246. doi: 10.3934/dcds.2020276 
2019 Impact Factor: 1.338
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