The nonlinear dynamics of the damped and driven Toda chain. III: Classification of the nonlinear resonances and local bifurcations

DOI10.1016/0167-2789(91)90145-YzbMath0736.34046OpenAlexW1618286447MaRDI QIDQ1181354

Werner Lauterborn, Karlheinz Geist

Publication date: 27 June 1992

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(91)90145-y

zbMATH Keywords

bifurcationresonanceeigenvalue spectrumperiod-doubling bifurcationsdynamics of damped and driven Toda chains

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical systems and ergodic theory (37-XX)

Related Items (3)

Dynamics of non-autonomous oscillator with a controlled phase and frequency of external forcing ⋮ Chaos and hyperchaos in coupled antiphase driven Toda oscillators ⋮ Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay

Cites Work

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• The nonlinear dynamics of the damped and driven Toda chain. I: Energy bifurcation diagrams
• On the continuability of periodic orbits of parametrized three- dimensional differential equations
• On the global structure of period doubling flows
• Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures
• The nonlinear dynamics of the damped and driven Toda chain. II: Fourier and Lyapunov analysis of tori
• Comparison of Different Methods for Computing Lyapunov Exponents

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