On the Hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in R4

Autor: Jiazhong Yang, Marco Antonio Teixeira, Jeroen S. W. Lamb, Ricardo Miranda Martins, Maurício Firmino Silva Lima

Publikováno v: Journal of Differential Equations. 269:11366-11395

This paper addresses the question whether normal forms of smooth reversible vector fields in R 4 at an elliptic equilibrium possess a formal Hamiltonian structure. In the non-resonant case we establish a formal conjugacy between reversible and Hamilt

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a70c1ccc801e213fe11dbb355badc99d
https://doi.org/10.1016/j.jde.2020.08.034

Conditioned Lyapunov exponents for random dynamical systems

Autor: Jeroen S. W. Lamb, Martin Rasmussen, Maximilian Engel

Publikováno v: Transactions of the American Mathematical Society. 372:6343-6370

We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to tra-jectories that stay within a bounded domain for asymptotically long times. This is motivated by thedesire to characterize local dynamical properties in the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::faad9e27acf37a21717ded40ab824dbc
https://doi.org/10.1090/tran/7803

Asymptotic estimates of SARS-CoV-2 infection counts and their sensitivity to stochastic perturbation

Autor: Oliver J. Hulme, Jeroen S. W. Lamb, Yuzuru Sato, Erica L. Thompson, Davide Faranda, Isaac Pérez Castillo, Aglaé Jézéquel

Publikováno v: Chaos: An Interdisciplinary Journal of Nonlinear Science
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020, 30 (5), pp.051107. ⟨10.1063/5.0008834⟩
Chaos
Chaos: An Interdisciplinary Journal of Nonlinear Science, American Institute of Physics, 2020, 30 (5), pp.051107. ⟨10.1063/5.0008834⟩

International audience; Despite the importance of having robust estimates of the time-asymptotic total number of infections, early estimates of COVID-19 show enormous fluctuations. Using COVID-19 data from different countries, we show that prediction

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::145c0b5fa2a9bf966f94fef0c80d1454
https://hal.science/hal-02668288

A random dynamical systems perspective on stochastic resonance

Autor: Jeroen S. W. Lamb, Anna Maria Cherubini, Yuzuru Sato, Martin Rasmussen

Publikováno v: Nonlinearity. 30:2835-2853

We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a nonautonomous forcin

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::03f39c7c25f9b3a02a417fbff1d78eb8
https://doi.org/10.1088/1361-6544/aa72bd

Hopf bifurcation with additive noise

Autor: Maximilian Engel, Martin Rasmussen, Thai Son Doan, Jeroen S. W. Lamb

We consider the dynamics of a two-dimensional ordinary differential equation exhibiting a Hopf bifurcation subject to additive white noise and identify three dynamical phases: (I) a random attractor with uniform synchronisation of trajectories, (II)

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c7e54edb038ed4f9ecda0e31e40d8e36
http://hdl.handle.net/10044/1/62264