Averaging Methods for the Phase Shift of Arbitrarily Perturbed Strongly Nonlinear Oscillators with an Application to Capture

DOI10.1137/0151058zbMath0731.34046OpenAlexW2022486756MaRDI QIDQ3356687

F. Jay Bourland, Richard Haberman, William L. Kath

Publication date: 1991

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0151058

zbMATH Keywords

nonlinear oscillators perturbation method basin of attraction averaging

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Nonlinear dynamics in mechanics (70K99) Singular perturbations for ordinary differential equations (34E15)

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Logarithmic correction to the probability of capture for dissipatively perturbed Hamiltonian systems ⋮ Connection across a Separatrix with Dissipation ⋮ Phase change and order 2 averaging for one-frequency systems with separatrix crossing* ⋮ Slow passage through a transcritical bifurcation for Hamiltonian systems and the change in action due to a nonhyperbolic homoclinic orbit ⋮ Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators ⋮ Averaged equations for injection locked semiconductor lasers ⋮ Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators

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