Publications – Dynamical Systems at Imperial College London (DynamIC)

George Chappelle and Martin Rasmussen, Rate-induced phenomena in dynamical systems with attracting limit cycles. DynamIC Preprint 2024-4
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
Matthieu Astorg and Fabrizio Bianchi, Bifurcations in families of polynomial skew products. DynamIC Preprint 2018-1
Alexander M. Henderson, Eric J. Olson, James C. Robinson, and Nicholas Sharples, Equi-homogeneity, Assouad dimension and non-autonomous dynamics. DynamIC Preprint 2014-7

2024

Lea Oljača, Peter Ashwin, and Martin Rasmussen, Measure and statistical attractors for nonautonomous dynamical systems, Journal of Dynamics and Differential Equations 36, 3 (2024), 2375−2411. Article MathSciNet

2023

George Chappelle, Alan Hastings, and Martin Rasmussen, Pool dynamics of time-dependent compartmental systems with application to the terrestrial carbon cycle, Journal of the Royal Society Interface 20(2023), 20220843. Article

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

Iacopo P. Longo, Carmen Núñez, Rafael Obaya, and Martin Rasmussen, Rate-induced tipping and saddle-node bifurcation for quadratic differential equations with nonautonomous asymptotic dynamics, SIAM Journal on Applied Dynamical Systems 20, 1 (2021), 500−540. Article MathSciNet Preprint
Moussa Ndour, Kathrin Padberg-Gehle, and Martin Rasmussen, Spectral early-warning signals for sudden changes in time-dependent flow patterns., Fluids 6(2021), 49. Article Preprint

2020

Genadi Levin, Weixiao Shen, and Sebastian van Strien, Positive transversality via transfer operators and holomorphic motions with applications to monotonicity for interval maps, Nonlinearity 33, 8 (2020), 3970−4012. Article MathSciNet

2017

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
Thai Son Doan, Kenneth J. Palmer, and Martin Rasmussen, The Bohl spectrum for linear nonautonomous differential equations, Journal of Dynamics and Differential Equations 29, 4 (2017), 1459−1485. Article MathSciNet Preprint

2016

Martin Rasmussen, Alan Hastings, Matthew J. Smith, Folashade B. Agusto, Benito M. Chen-Charpentier, Forrest M. Hoffman, Jiang Jiang, Katherine E. O. Todd-Brown, Ying Wang, Ying-Ping Wang, and Yiqi Luo, Transit times and mean ages for nonautonomous and autonomous compartmental systems, Journal of Mathematical Biology 73, 6−7 (2016), 1379−1398. 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
Patrick Bonckaert, Peter De Maesschalck, Thai Son Doan, and Stefan Siegmund, Partial linearization for planar nonautonomous differential equations, Journal of Differential Equations 258, 5 (2015), 1618−1652. 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

2014

Nguyen Dinh Cong, Thai Son Doan, Stefan Siegmund, and Hoang The Tuan, On stable manifolds for planar fractional differential equations, Applied Mathematics and Computation 226(2014), 157−168. Article MathSciNet
Tiago Pereira, Jaap Eldering, Martin Rasmussen, and Alexei Veneziani, Towards a theory for diffusive coupling functions allowing persistent synchronization, Nonlinearity 27, 3 (2014), 501−525. Article MathSciNet Preprint
Dmitry Turaev, Christopher Warner, and Sergey Zelik, Energy growth for a nonlinear oscillator coupled to a monochromatic wave, Regular and Chaotic Dynamics 19, 4 (2014), 513−522. Article MathSciNet

2013

Thai Son Doan, Anke Kalauch, and Stefan Siegmund, A constructive approach to linear Lyapunov functions for positive switched systems using Collatz-Wielandt sets, Institute of Electrical and Electronics Engineers. Transactions on Automatic Control 58, 3 (2013), 748−751. 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
James C. Robinson and Nicholas Sharples, Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations, Journal of Differential Equations 254, 10 (2013), 4144−4167. 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
Peter Giesl and Martin Rasmussen, Areas of attraction for nonautonomous differential equations on finite time intervals, Journal of Mathematical Analysis and Applications 390, 1 (2012), 27−46. Article MathSciNet
Peter E. Kloeden, Christian Pötzsche, and Martin Rasmussen, Limitations of pullback attractors for processes, Journal of Difference Equations and Applications 18, 4 (2012), 693−701. Article MathSciNet

2011

Peter Giesl and Martin Rasmussen, A note on almost periodic variational equations, Communications on Pure and Applied Analysis 10, 3 (2011), 983−994. Article MathSciNet
Peter E. Kloeden and Martin Rasmussen, Nonautonomous dynamical systems, Mathematical Surveys and Monographs 176, American Mathematical Society, Providence, RI, 2011. MathSciNet

2010

Fritz Colonius, Thorsten Hüls, and Martin Rasmussen, Connecting orbits in perturbed systems, Nonlinear Dynamics 59, 4 (2010), 569−578. Article MathSciNet
Christian Pötzsche and Martin Rasmussen, Computation of integral manifolds for Carathéodory differential equations, IMA Journal of Numerical Analysis 30, 2 (2010), 401−430. Article MathSciNet
Martin Rasmussen, An alternative approach to Sacker-Sell spectral theory, Journal of Difference Equations and Applications 16, 2−3 (2010), 227−242. Article MathSciNet
Martin Rasmussen, Finite-time attractivity and bifurcation for nonautonomous differential equations, Differential Equations and Dynamical Systems 18, 1−2 (2010), 57−78. Article MathSciNet

2009

Christian Pötzsche and Martin Rasmussen, Computation of nonautonomous invariant and inertial manifolds, Numerische Mathematik 112, 3 (2009), 449−483. Article MathSciNet
Christian Pötzsche and Martin Rasmussen, Hibernation prevents chaos: a logistic case study, in: Difference equations and applications (M. Bohner, Z. Doslá, G. Ladas, M. Ünal, A. Zafer), 259−274, Uğur-Bahçeşehir Univ. Publ. Co., Istanbul, 2009. MathSciNet
Martin Rasmussen, Dichotomy spectra and Morse decompositions of linear nonautonomous differential equations, Journal of Differential Equations 246, 6 (2009), 2242−2263. Article MathSciNet

2008

Fritz Colonius, Peter E. Kloeden, and Martin Rasmussen, Morse spectrum for nonautonomous differential equations, Stochastics and Dynamics 8, 3 (2008), 351−363. Article MathSciNet
Vassili Gelfreich and Dmitry Turaev, Unbounded energy growth in Hamiltonian systems with a slowly varying parameter, Communications in Mathematical Physics 283, 3 (2008), 769−794. Article MathSciNet
Peter Giesl and Martin Rasmussen, Borg's criterion for almost periodic differential equations, Nonlinear Analysis. Theory, Methods & Applications 69, 11 (2008), 3722−3733. Article MathSciNet
Martin Rasmussen, All-time Morse decompositions of linear nonautonomous dynamical systems, Proceedings of the American Mathematical Society 136, 3 (2008), 1045−1055. Article MathSciNet
Martin Rasmussen, Bifurcations of asymptotically autonomous differential equations, Set-Valued Analysis 16, 7−8 (2008), 821−849. Article MathSciNet

2007

Martin Rasmussen, Nonautonomous bifurcation patterns for one-dimensional differential equations, Journal of Differential Equations 234, 1 (2007), 267−288. Article MathSciNet
Martin Rasmussen, Attractivity and bifurcation for nonautonomous dynamical systems, Lecture Notes in Mathematics 1907, Springer, Berlin, 2007. MathSciNet
Martin Rasmussen, Morse decompositions of nonautonomous dynamical systems, Transactions of the American Mathematical Society 359, 10 (2007), 5091−5115. Article MathSciNet

2006

Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Invariant manifolds as pullback attractors of nonautonomous differential equations, Discrete and Continuous Dynamical Systems A 15, 2 (2006), 579−596. Article MathSciNet
Tobias H. Jäger and Jaroslav Stark, Towards a classification for quasiperiodically forced circle homeomorphisms, Journal of the London Mathematical Society 73, 3 (2006), 727−744. Article MathSciNet
Christian Pötzsche and Martin Rasmussen, Taylor approximation of integral manifolds, Journal of Dynamics and Differential Equations 18, 2 (2006), 427−460. Article MathSciNet
Martin Rasmussen, Towards a bifurcation theory for nonautonomous difference equations, Journal of Difference Equations and Applications 12, 3−4 (2006), 297−312. Article MathSciNet

2005

Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Approximation of attractors of nonautonomous dynamical systems, Discrete and Continuous Dynamical Systems B 5, 2 (2005), 215−238. Article MathSciNet
Bernd Aulbach, Martin Rasmussen, and Stefan Siegmund, Invariant manifolds as pullback attractors of nonautonomous difference equations, in: Proceedings of the Eighth International Conference on Difference Equations and Applications (S. Elaydi, G. Ladas, B. Aulbach, O. Dosly), 23−37, CRC, Boca Raton, 2005. Article MathSciNet
Christian Pötzsche and Martin Rasmussen, Taylor approximation of invariant fiber bundles for nonautonomous difference equations, Nonlinear Analysis. Theory, Methods & Applications 60, 7 (2005), 1303−1330. Article MathSciNet
Christian Pötzsche and Martin Rasmussen, Local approximation of invariant fiber bundles: an algorithmic approach, in: Difference equations and discrete dynamical systems (L. Allen, B. Aulbach, S. Elaydi, R. Sacker), 155−170, World Scientific, Singapore, 2005. Article MathSciNet

2003

Jaroslav Stark, Transitive sets for quasi-periodically forced monotone maps, Dynamical Systems 18, 4 (2003), 351−364. Article MathSciNet