Melnikov method for homoclinic bifurcation in nonlinear impact oscillators
From MaRDI portal
Publication:814317
DOI10.1016/j.camwa.2005.03.007zbMath1097.37043OpenAlexW2043378533MaRDI QIDQ814317
Publication date: 6 February 2006
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2005.03.007
Bifurcation theory for ordinary differential equations (34C23) Bifurcations and instability for nonlinear problems in mechanics (70K50) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)
Related Items
On the number of limit cycles in small perturbations of a piecewise linear Hamiltonian system with a heteroclinic loop ⋮ Quasi-periodic solutions and homoclinic bifurcation in an impact inverted pendulum ⋮ Melnikov Theory for Two-Dimensional Manifolds in Three-Dimensional Flows ⋮ Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones ⋮ Chaotic threshold for a class of impulsive differential system ⋮ Limit cycles near generalized homoclinic and double homoclinic loops in piecewise smooth systems ⋮ Chaotic threshold for non-smooth system with multiple impulse effect ⋮ Centers and isochronous centers of a class of quasi-analytic switching systems ⋮ The Melnikov method of heteroclinic orbits for a class of planar hybrid piecewise-smooth systems and application ⋮ Frequency and amplitude identification of weak signal based on the limit system of smooth and discontinuous oscillator ⋮ Limit cycles bifurcate from centers of discontinuous quadratic systems ⋮ Type I periodic motions for nonlinear impact oscillators ⋮ Melnikov-type method for chaos in a class of hybrid piecewise-smooth systems with impact and noise excitation under unilateral rigid constraint ⋮ Viscoelastic string-beam coupled vibro-impact system: modeling and dynamic analysis ⋮ A new vibro-impact bistable oscillator with an adjustable rigid wall ⋮ Bifurcation of Limit Cycles from a Class of Piecewise Smooth Systems with Two Vertical Straight Lines of Singularity ⋮ Subharmonic Bifurcation for a Nonsmooth Oscillator ⋮ Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux ⋮ Center and isochronous center conditions for switching systems associated with elementary singular points ⋮ Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop ⋮ Impact oscillators with homoclinic orbit tangent to the wall ⋮ DYNAMICS OF A DAMPING OSCILLATOR WITH IMPACT AND IMPULSIVE EXCITATION ⋮ Computing the heteroclinic bifurcation curves in predator-prey systems with ratio-dependent functional response ⋮ Homoclinic bifurcations and chaotic dynamics for a piecewise linear system under a periodic excitation and a viscous damping ⋮ Homoclinic bifurcation in a quasiperiodically excited impact inverted pendulum ⋮ The Melnikov method for detecting chaotic dynamics in a planar hybrid piecewise-smooth system with a switching manifold ⋮ Subharmonic Melnikov theory for degenerate resonance systems and its application ⋮ Limit cycles bifurcating from piecewise quadratic systems separated by a straight line ⋮ ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS ⋮ Bifurcation of periodic orbits in a class of planar Filippov systems ⋮ Persistence of periodic orbits in periodically forced impact systems ⋮ GENERALIZED SEMIFLOWS AND CHAOS IN MULTIVALUED DYNAMICAL SYSTEMS ⋮ Melnikov-Type Method for a Class of Discontinuous Planar Systems and Applications ⋮ Bifurcation and chaos near sliding homoclinics ⋮ Asymmetric type II periodic motions for nonlinear impact oscillators ⋮ Codimension 2 bifurcation of twisted double homoclinic loops ⋮ Limit Cycles Near a Piecewise Smooth Generalized Homoclinic Loop with a Nonelementary Singular Point ⋮ An example of chaotic behaviour in presence of a sliding homoclinic orbit ⋮ Suppressing homoclinic chaos for a weak periodically excited non-smooth oscillator ⋮ Chaotic dynamics of the vibro-impact system under bounded noise perturbation ⋮ Numerical computation of connecting orbits in planar piecewise smooth dynamical system ⋮ Melnikov Method for a Three-Zonal Planar Hybrid Piecewise-Smooth System and Application ⋮ Melnikov Method for a Class of Planar Hybrid Piecewise-Smooth Systems ⋮ Chaos detection of Duffing system with fractional-order derivative by Melnikov method ⋮ Dynamics of a vibro-impact system by the global analysis method in parameter-state space ⋮ On the chaotic behavior of non-flat billiards ⋮ Melnikov's method for a general nonlinear vibro-impact oscillator ⋮ Chaotic threshold of a class of hybrid piecewise-smooth system by an impulsive effect via Melnikov-type function ⋮ Computing Melnikov Curves for Periodically Perturbed Piecewise Smooth Oscillators ⋮ Bifurcation of safe basins and chaos in nonlinear vibroimpact oscillator under harmonic and bounded noise excitations
Cites Work
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Bifurcations of subharmonics
- The transition to chaos in a simple mechanical system
- Local analysis of \(C\)-bifurcations in \(n\)-dimensional piecewise-smooth dynamical systems
- Period-doubling induced chaotic motion in the LR model of a horizontal impact oscillator
- Global chaos in a periodically forced, linear system with a dead-zone restoring force
- On normal form calculations in impact oscillators
- A periodically forced piecewise linear oscillator
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item