Chaotic behavior in differential equations driven by a Brownian motion
type: Item
instance of: scholarly article
title: Chaotic behavior in differential equations driven by a Brownian motion
zbMATH Open document ID: 1231.34080
author: Kening Lu
author: Qiudong Wang
published in: Journal of Differential Equations
publication date: 2011-10-12T00:00:00Z
review text: The authors examine the chaotic behaviour exhibited by ordinary differential equations having a homoclinic orbit to a saddle point under unbounded random forcing driven by Brownian motion. The approach is `sample-wise', though the need for using the features of the Brownian motion as a whole is noted. Application is made to the Duffing equation and the non-linear pendulum.
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 5957028
zbMATH Keywords: Brownian motion
zbMATH Keywords: Wiener shift
zbMATH Keywords: unbounded stochastic forcing
zbMATH Keywords: chaotic behavior
zbMATH Keywords: topological horseshoe
zbMATH Keywords: Cantor sets
zbMATH Keywords: random Melnikov function
zbMATH Keywords: Duffing equation
zbMATH Keywords: pendulum equation
reviewed by: Andrew Dale
MaRDI profile type: Publication
full work available at URL: j.jde.2011.05.032
OpenAlex ID: W2074189340
cites work: QUASIRANDOM DYNAMICAL SYSTEMS. III QUASIRANDOM OSCILLATIONS OF ONE-DIMENSIONAL OSCILLATORS
cites work: Q4210478
cites work: The ring principle in problems of interaction between two self- oscillating systems
cites work: Chaos in the Duffing equation
cites work: Q5765944
cites work: A geometric criterion for positive topological entropy
cites work: Horseshoes and the Conley index spectrum. II: The theorem is sharp
cites work: Horseshoes and the Conley index spectrum
cites work: Q3948194
cites work: An example of bifurcation to homoclinic orbits
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
cites work: A nonlinear oscillator with a strange attractor
cites work: Topological horseshoes
cites work: A second order differential equation with singular solutions
cites work: Sternberg theorems for random dynamical systems
cites work: Chaos in differential equations driven by a nonautonomous force
cites work: Q5508470
cites work: Isolating neighborhoods and chaos
cites work: Stable and Random Motions in Dynamical Systems
cites work: Melnikov Transforms, Bernoulli Bundles, and Almost Periodic Perturbations
cites work: Exponential dichotomies and transversal homoclinic points
cites work: Exponential Dichotomies for Almost Periodic Equations
cites work: Chaos in almost periodic systems
cites work: Q5518129
cites work: Differentiable dynamical systems
cites work: Chaotic solutions of systems with almost periodic forcing
cites work: Q5577414
cites work: Q5551675
cites work: Q5509205
cites work: A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
cites work: ON A POINCARÉ-BIRKHOFF PROBLEM
cites work: Q4264342
cites work: Q4947577
cites work: Q3844116
cites work: The Conley index and symbolic dynamics
cites work: Global bifurcations and chaos. Analytical methods
cites work: Dynamics of homoclinic tangles in periodically perturbed second-order equations
cites work: Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems
DOI: 10.1016/J.JDE.2011.05.032
description: scientific article; zbMATH DE number 5957028