The origins of chaos in a modified Van der Pol oscillator

DOI10.1016/0167-2789(91)90091-MzbMath0726.58033MaRDI QIDQ804043

N. E. Zubov

Publication date: 1991

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

zbMATH Keywords

Hopf bifurcationdynamical systemchaotic behaviourhomoclinic orbitglobal dynamicsVan der Pol oscillatorShil'nikov mechanism

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Applications of global analysis to the sciences (58Z05) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Attractors of solutions to ordinary differential equations (34D45) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (9)

Topology from time series ⋮ GLUING BIFURCATIONS IN CHUA OSCILLATOR ⋮ Homoclinic phenomena in opto-thermal bistability with localized absorption ⋮ Nonlinear time series analysis of jerk congenital nystagmus ⋮ Robust estimation of tangent maps and Liapunov spectra ⋮ A case study for homoclinic chaos in an autonomous electronic circuit. A trip from Takens-Bogdanov to Hopf-Sil'nikov ⋮ Disordered fluid motion in a small closed system ⋮ Local analysis of time series from the oscillatory electrocatalytic reduction of hydrogen peroxide ⋮ Analysis of static and dynamic bifurcations from a feedback systems perspective

Cites Work

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• Bifurcation phenomena near homoclinic systems: A two-parameter analysis
• Asymptotic chaos
• Extracting qualitative dynamics from experimental data
• Classification and unfoldings of degenerate Hopf bifurcations
• Singularities of vector fields
• An experimental observation of a new type of intermittency
• Topological dimension and local coordinates from time series data
• Time-series analysis

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