Chaos in the Duffing equation

DOI10.1006/JDEQ.1993.1013zbMath0772.34040OpenAlexW1967531003MaRDI QIDQ1208697

Flaviano Battelli, Kenneth James Palmer

Publication date: 16 May 1993

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.1993.1013

zbMATH Keywords

chaosheteroclinic orbitexponential dichotomiesDuffing equationhomoclinicsingularly perturbed equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcations and instability for nonlinear problems in mechanics (70K50) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Dynamical systems and ergodic theory (37-XX)

Related Items (31)

Exponential dichotomies, the Fredholm alternative, and transverse homoclinic orbits in partial functional differential equations ⋮ Superlinear indefinite equations on the real line and chaotic dynamics ⋮ Many periodic solutions for pendulum-type equations ⋮ Heteroclinic chaotic behavior driven by a Brownian motion ⋮ Validated numerics for equilibria of analytic vector fields: Invariant manifolds and connecting orbits ⋮ Unnamed Item ⋮ Exponential dichotomies and transversal homoclinic orbits in degenerate cases ⋮ Chaotic dynamics in a vertically driven planar pendulum ⋮ Exponential dichotomies in linear systems with a small parameter ⋮ Numerical solution of Duffing equation by using an improved Taylor matrix method ⋮ A geometric criterion for adiabatic chaos ⋮ Unnamed Item ⋮ Multiple families of bounded solutions near perturbed homoclinic orbits, application to a nonlinear wave equation ⋮ Genericity of exponential dichotomy for two-dimensional differential systems ⋮ Chaotic behavior in differential equations driven by a Brownian motion ⋮ Chaos in singular impulsive O.D.E. ⋮ A nonconvex dissipative system and its applications. I ⋮ Multiple homoclinic solutions for singular differential equations ⋮ Impulsive synchronization of coupled dynamical networks with nonidentical Duffing oscillators and coupling delays ⋮ Transverse intersection of invariant manifolds in singular systems. ⋮ Chaos in a Periodically Perturbed Second-Order Equation with Signum Nonlinearity ⋮ Chaos in singular systems ⋮ Homoclinic Solutions and Chaos in Ordinary Differential Equations with Singular Perturbations ⋮ Bifurcation from homoclinic to periodic solutions in singular ordinary differential equations ⋮ Heteroclinic period blow-up in certain symmetric ordinary differential equations ⋮ Periodic oscillations of forced pendulums with very small length ⋮ Rigorous chaos verification in discrete dynamical systems ⋮ Exponential dichotomies and Melnikov functions for singularly perturbed systems ⋮ Heteroclinic orbits in singular systems: A unifying approach ⋮ Monotonous property of non-oscillations of the damped Duffing's equation ⋮ Bifurcation from a periodic orbit in perturbed planar Hamiltonian systems.

This page was built for publication: Chaos in the Duffing equation