Stochastic global bifurcation in perturbed Hamiltonian systems
type: Item
instance of: scholarly article
title: Stochastic global bifurcation in perturbed Hamiltonian systems
zbMATH Open document ID: 1069.34077
author: Lora Billings
author: Erik Bollt
author: Ira B. Schwartz
author: David S. Morgan
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-02-23T00:00:00Z
review text: This paper deals with two perturbed Hamiltonian systems in which chaos-like dynamics can be induced by stochastic perturbations. For ordinary differential equations arising from two different fields, the population of epidemic model and the single mode periodically modulated laser model, the authors show that both systems can be reduced to the same weakly perturbed Hamiltonian system and have similar bifurcation structure and manifold structure that includes bi-instability and partially formed heteroclinic connections. In the presence of a bi-stability, they discuss how noise can induce a global bifurcation and chaos-like dynamics which exhibits mixed mode behavior of the original bi-stable solutions, using numerical approximations to the transport between basins.
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 37J20
zbMATH DE Number: 2046175
zbMATH Keywords: stochastic dynamical systems
zbMATH Keywords: Hamiltonian
zbMATH Keywords: bifurcation
zbMATH Keywords: chaos
reviewed by: Makiko Nisio
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2046175