The method of Melnikov for perturbations of multi-degree-of-freedom Hamiltonian systems

DOI10.1088/0951-7715/12/4/304zbMath0967.34042OpenAlexW1963794568MaRDI QIDQ4265663

Publication date: 20 August 2001

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/12/4/304

zbMATH Keywords

Melnikov method transversal homoclinic orbits

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Forced motions for nonlinear problems in mechanics (70K40) Hamilton's equations (70H05) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

Related Items (21)

Melnikov processes and chaos in randomly perturbed dynamical systems ⋮ Melnikov Theory for Two-Dimensional Manifolds in Three-Dimensional Flows ⋮ Bifurcation of homoclinic orbits with saddle-center equilibrium ⋮ Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations ⋮ Homoclinic flip bifurcation with a nonhyperbolic equilibrium ⋮ Gain-loss-driven travelling waves in PT-symmetric nonlinear metamaterials ⋮ Homoclinic flip bifurcations accompanied by transcritical bifurcation ⋮ Resonant chaotic motions of a buckled rectangular thin plate with parametrically and externally excitations ⋮ Resonant Chaotic Dynamics of a Symmetric Cross-Ply Composite Laminated Plate Under Transverse and In-Plane Excitations ⋮ Transverse intersection of invariant manifolds in perturbed multi-symplectic systems ⋮ Double excitation multi-stability and multi-pulse chaotic vibrations of a bistable asymmetric laminated composite square panels under foundation force ⋮ Coexistence of bistable multi-pulse chaotic motions with large amplitude vibrations in buckled sandwich plate under transverse and in-plane excitations ⋮ Transient Chaos in Coupled Oscillators with Shape Deformable Potential ⋮ On the stability of a domain-wall brane model ⋮ The extended Melnikov method for non-autonomous nonlinear dynamical systems and application to multi-pulse chaotic dynamics of a buckled thin plate ⋮ Detection of symmetric homoclinic orbits to saddle-centres in reversible systems ⋮ Analytic and algebraic conditions for bifurcations of homoclinic orbits I: Saddle equilibria ⋮ THEORIES OF MULTI-PULSE GLOBAL BIFURCATIONS FOR HIGH-DIMENSIONAL SYSTEMS AND APPLICATION TO CANTILEVER BEAM ⋮ Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations ⋮ Weak finite-time Melnikov theory and three-dimensional viscous perturbations of Euler flows ⋮ From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics

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