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Random dynamical systems
Preprints
- Jeroen S. W. Lamb, Martin Rasmussen, and Wei Hao Tey, Attractors of Linear Maps with Bounded Noise. DynamIC Preprint 2023-2
- Konstantinos Kourliouros, Jeroen S. W. Lamb, Martin Rasmussen, Wei Hao Tey, Kalle G. Timperi, and Dmitry Turaev, Persistence of minimal invariant sets for certain set-valued dynamical systems: a boundary mapping approach. DynamIC Preprint 2023-1
- Matheus M. Castro, Vincent P. H. Goverse, Jeroen S. W. Lamb, and Martin Rasmussen, On the quasi-ergodicity of absorbing Markov chains with unbounded transition densities, including random logistic maps with escape. DynamIC Preprint 2022-2
- Matheus M. Castro, Dennis Chemnitz, Hugo Chu, Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, The Lyapunov spectrum for conditioned random dynamical systems. DynamIC Preprint 2022-1
- Matheus M. Castro, Jeroen S. W. Lamb, Guillermo Olicón Méndez, and Martin Rasmussen, Existence and uniqueness of quasi-stationary and quasi-ergodic measures for absorbing Markov chains: a Banach lattice approach . DynamIC Preprint 2021-3
- Mickael D. Chekroun, Jeroen S.W. Lamb, Christian J. Pangerl, and Martin Rasmussen, A Girsanov approach to slow parameterizing manifolds in the presence of noise. DynamIC Preprint 2019-7
- Flavia Remo, Gabriel Fuhrmann, and Tobias Jäger, On the effect of forcing of fold bifurcations and early-warning signals in population dynamics. DynamIC Preprint 2019-6
- Thai Son Doan, Jeroen S.W. Lamb, Julian Newman, and Martin Rasmussen, Classification of random circle homeomorphisms up to topological conjugacy. DynamIC Preprint 2018-3
- Julian Newman, Synchronisation of almost all trajectories of a random dynamical system. DynamIC Preprint 2015-12
- Julian Newman, Synchronisation in Invertible Random Dynamical Systems on the Circle. DynamIC Preprint 2015-11
2022
- George Chappelle, Alan Hastings, and Martin Rasmussen, Occupancy times for time-dependent stage-structured models, Journal of Mathematical Biology 84, 3 (2022), Paper No. 16, 17. Article MathSciNet Preprint
2021
- Fritz Colonius and Martin Rasmussen, Quasi-ergodic limits for finite absorbing Markov chains, Linear Algebra and its Applications 609(2021), 253−288. Article MathSciNet Preprint
2020
- Peter Giesl, Boumediene Hamzi, Martin Rasmussen, and Kevin Webster, Approximation of Lyapunov functions from noisy data, Journal of Computational Dynamics 7, 1 (2020), 57−81. Article MathSciNet Preprint
2019
- Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle, Communications in Mathematical Physics 365, 3 (2019), 935−942. Article MathSciNet Preprint
- Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Conditioned Lyapunov exponents for random dynamical systems, Transactions of the American Mathematical Society 372, 9 (2019), 6343−6370. Article MathSciNet Preprint
2018
- Thai Son Doan, Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Hopf bifurcation with additive noise, Nonlinearity 31, 10 (2018), 4567−4601. Article MathSciNet Preprint
- Christian Kuehn, Giuseppe Malavolta, and Martin Rasmussen, Early-warning signals for bifurcations in random dynamical systems with bounded noise, Journal of Mathematical Analysis and Applications 464, 1 (2018), 58−77. Article MathSciNet Preprint
- Julian Newman, Necessary and sufficient conditions for stable synchronization in random dynamical systems, Ergodic Theory and Dynamical Systems 38, 5 (2018), 1857−1875. Article MathSciNet Preprint
2017
- Mark Callaway, Thai Son Doan, Jeroen S. W. Lamb, and Martin Rasmussen, The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise, Annales de l'Institut Henri Poincaré Probabilités et Statistiques 53, 4 (2017), 1548−1574. Article MathSciNet Preprint
- Anna Maria Cherubini, Jeroen S. W. Lamb, Martin Rasmussen, and Yuzuru Sato, A random dynamical systems perspective on stochastic resonance, Nonlinearity 30, 7 (2017), 2835−2853. Article MathSciNet Preprint
2015
- Vasso Anagnostopoulou, Tobias Jäger, and Gerhard Keller, A model for the nonautonomous Hopf bifurcation, Nonlinearity 28, 7 (2015), 2587−2616. MathSciNet Preprint
- Nguyen Dinh Cong, Thai Son Doan, and Stefan Siegmund, On Lyapunov exponents of difference equations with random delay, Discrete and Continuous Dynamical Systems B 20, 3 (2015), 861−874. Article MathSciNet
- Thai Son Doan, Martin Rasmussen, and Peter E. Kloeden, The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor, Discrete and Continuous Dynamical Systems B 20, 3 (2015), 875−887. Article MathSciNet Preprint
- Jeroen S. W. Lamb, Martin Rasmussen, and Christian S. Rodrigues, Topological bifurcations of minimal invariant sets for set-valued dynamical systems, Proceedings of the American Mathematical Society 143, 9 (2015), 3927−3937. Article MathSciNet Preprint
2014
- Nguyen Dinh Cong, Thai Son Doan, and Hoang The Tuan, On fractional Lyapunov exponent for solutions of linear fractional differential equations, Fractional Calculus and Applied Analysis 17, 2 (2014), 285−306. Article MathSciNet
2013
- Kamaludin Dingle, Jeroen S. W. Lamb, and Joan-Andreu Lázaro-Camí, Knudsen's law and random billiards in irrational triangles, Nonlinearity 26, 2 (2013), 369−388. Article MathSciNet
- Thai Son Doan and Stefan Siegmund, Differential equations with random delay, in: Infinite dimensional dynamical systems, Fields Institute Communications, 279−303, Springer, New York, 2013. Article MathSciNet
- Peter E. Kloeden, Christian Pötzsche, and Martin Rasmussen, Discrete-time nonautonomous dynamical systems, in: Stability and bifurcation theory for non-autonomous differential equations, Lecture Notes in Mathematics, 35−102, Springer, Heidelberg, 2013. Article MathSciNet
- Weixiao Shen and Sebastian van Strien, On stochastic stability of expanding circle maps with neutral fixed points, Dynamical Systems 28, 3 (2013), 423−452. Article MathSciNet
2012
- Vasso Anagnostopoulou and Tobias Jäger, Nonautonomous saddle-node bifurcations: random and deterministic forcing, Journal of Differential Equations 253, 2 (2012), 379−399. Article MathSciNet
2010
- Fritz Colonius, Thorsten Hüls, and Martin Rasmussen, Connecting orbits in perturbed systems, Nonlinear Dynamics 59, 4 (2010), 569−578. Article MathSciNet
2008
- Yongluo Cao, Stefano Luzzatto, and Isabel Rios, Uniform hyperbolicity for random maps with positive Lyapunov exponents, Proceedings of the American Mathematical Society 136, 10 (2008), 3591−3600. Article MathSciNet
2003
- Jaroslav Stark, David S. Broomhead, Mike E. Davies, and Jeremy P. Huke, Delay embeddings for forced systems II. Stochastic forcing, Journal of Nonlinear Science 13, 6 (2003), 519−577. Article MathSciNet
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