Home Publications Undergraduates Postgraduates Postdocs Calendar Contact

STAFF
  Jeroen Lamb  
  Martin Rasmussen  
  Dmitry Turaev  
  Sebastian van Strien  
RESEARCHERS
Mike Field
POSTDOCS
Vasso Anagnostopoulou
Trevor Clark
Julian Newman
Janosch Rieger
PHD STUDENTS
Alex Athorne
Sajjad Bakrani Balani
Maximilian Engel
Michael Hartl
Giuseppe Malavolta
Cezary Olszowiec
Christian Pangerl
Francesco Ricci
Matteo Tanzi
Kalle Timperi
VISITORS
Anna Maria Cherubini
Carlos Siquiera
Bill Speares
RELATED STAFF
Mauricio Barahona
Davoud Cheraghi
Jaap Eldering
John Elgin
Darryl Holm
Greg Pavliotis


DR MARTIN RASMUSSEN

Martin Rasmussen

Senior Lecturer in Mathematics

 
 

Phone: +44(207)59-42774
Room: 637 Huxley Building

PHD STUDENTS
Alex Athorne
Maximilian Engel
Michael Hartl
Giuseppe Malavolta
Christian Pangerl

POSTDOCS
Vasso Anagnostopoulou
Julian Newman
Janosch Rieger

Areas of interest


My research aims at the development of the Qualitative Theory of Nonautonomous and Random Dynamical Systems. In particular, I have made contributions to the following areas:
  • stability and attractor theory,
  • bifurcation theory,
  • theory of invariant manifolds, and
  • Morse decomposition theory.

Grants, Awards and Prizes

  • Marie Sklodowska-Curie Innovative Training Network on Critical Transitions in Complex Systems (co-PI with Jeroen Lamb), 2015–2019.
  • Marie Curie IEF Fellowship (Researcher: Janosch Rieger), 2015–2017.
  • EPSRC Grant New Directions for Research Leaders, 2013–2015.
  • Marie Curie IEF Fellowship (Researcher: Vasso Anagnostopoulou), 2013–2016.
  • Marie Curie IEF Fellowship (Researcher: Doan Thai Son, co-PI with Jeroen Lamb), 2013–2015.
  • EPSRC Career Acceleration Fellowship, 2010–2015.
  • Marie Curie IEF Fellowship (Researcher), 2008–2010.
  • Postdoctoral Grant from the State of Bavaria, 2006–2007, University of Augsburg.
  • The article Towards a Bifurcation Theory for Nonautonomous Difference Equations was awarded the prize of the best paper in 2006 by the International Society of Difference Equations (ISDE).
  • Grant for excellent undergraduate studies from the Department of Mathematics at the University of Augsburg, 1999–2000.

Publications

  • Books:
    • Peter E. Kloeden and Martin Rasmussen, Nonautonomous dynamical systems, Mathematical Surveys and Monographs 176, American Mathematical Society, Providence, 2011. MathSciNet
    • Martin Rasmussen, Attractivity and bifurcation for nonautonomous dynamical systems, Lecture Notes in Mathematics 1907, Springer, Berlin, 2007. MathSciNet
  • Submitted journal articles:
    • Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle. DynamIC Preprint 2016-6
    • Peter Giesl, Boumediene Hamzi, Martin Rasmussen, and Kevin N. Webster, Approximation of Lyapunov functions from noisy data. DynamIC Preprint 2016-1
    • Anna Maria Cherubini, Jeroen S.W. Lamb, Martin Rasmussen, and Yuzuru Sato, A random dynamical systems perspective on stochastic resonance. DynamIC Preprint 2015-6.
    • Martin Rasmussen, Janosch Rieger, and Kevin N. Webster, A reinterpretation of set differential equations as differential equations in a Banach space. DynamIC Preprint 2015-3.
    • Martin Rasmussen, Janosch Rieger, and Kevin N. Webster, Approximation of reachable sets using optimal control and support vector machines. DynamIC Preprint 2014-13.
  • Accepted journal articles:
    • 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, to appear in: Journal of Mathematical Biology. DynamIC Preprint 2015-7
    • Thai Son Doan, Kenneth J. Palmer, and Martin Rasmussen, The Bohl spectrum for linear nonautonomous differential equations, to appear in: Journal of Dynamics and Differential Equations DynamIC Preprint 2015-2.
    • 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, to appear in: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques DynamIC Preprint 2013-4.
  • Journal articles:
    • Ying-Ping Wang, Jiang Jiang, Benito Chen-Charpentier, Folashade B. Agusto, Alan Hastings, Forrest Hoffman, Martin Rasmussen, Matthew J. Smith, Katherine Todd-Brown, Ying Wang, Xia Xu, and Yiqi Luo, Responses of two nonlinear microbial models to warming and increased carbon input, Biogeosciences 13(2016), 887−902. Article
    • 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
    • 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
    • Ying-Ping Wang, Benito Chen, William R. Wieder, Yiqi Luo, Maria Leite, Belinda E. Medlyn, Martin Rasmussen, Matthew J. Smith, Folashade B. Agusto, and Forrest Hoffman, Oscillatory behavior of two nonlinear microbial models of soil carbon decomposition, Biogeosciences  11, 7 (2014), 1817−1831. Article
    • 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
    • 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
    • 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
    • Christian Pötzsche and Martin Rasmussen, Computation of nonautonomous invariant and inertial manifolds, Numerische Mathematik 112, 3 (2009), 449−483. Article MathSciNet
    • Martin Rasmussen, Dichotomy spectra and Morse decompositions of linear nonautonomous differential equations, Journal of Differential Equations 246, 6 (2009), 2242−2263. Article MathSciNet
    • Fritz Colonius, Peter E. Kloeden, and Martin Rasmussen, Morse spectrum for nonautonomous differential equations, Stochastics and Dynamics 8, 3 (2008), 351−363. 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
    • Martin Rasmussen, Nonautonomous bifurcation patterns for one-dimensional differential equations, Journal of Differential Equations 234, 1 (2007), 267−288. Article MathSciNet
    • Martin Rasmussen, Morse decompositions of nonautonomous dynamical systems, Transactions of the American Mathematical Society 359, 10 (2007), 5091−5115. Article MathSciNet
    • 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
    • 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
    • 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
    • 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
  • Articles in conference proceedings:
    • 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
    • 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
    • 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, 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
  • Miscellaneous:
    • Attractivity and Bifurcation for Nonautonomous Dynamical Systems, PhD Thesis, University of Augsburg, 2006, 190 pages.
    • Approximation von Attraktoren und Mannigfaltigkeiten nichtautonomer Systeme, Diploma Thesis, University of Augsburg, 2002, 119 pages. (PDF coloured, PDF monochrome, PS coloured, PS monochrome)
    • Bevölkerungsprognose für Augsburg 2000–2015 (with H. Glöckner), Beiträge zur Stadtentwicklung, Stadtforschung und Statistik 18, Stadt Augsburg, 2000, 386 pages.
Nonautonomous Dynamical Systems

Attractivity and Bifurcation for Nonautonomous Dynamical Systems