Mixed-mode oscillations and chaos from a simple second-order oscillator under weak periodic perturbation

DOI10.1016/J.PHYSLETA.2011.02.053zbMath1242.34063OpenAlexW2066743544MaRDI QIDQ432939

Kuniyasu Shimizu, Naohiko Inaba, Munehisa Sekikawa

Publication date: 4 July 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2011.02.053

zbMATH Keywords

chaosmixed-mode oscillationssubcritical Andronov-Hopf bifurcationthe driven Bonhoeffer-van der Pol oscillator

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Forced motions for nonlinear problems in mechanics (70K40) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Complex behavior and chaotic systems of ordinary differential equations (34C28) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (14)

Complex mixed-mode oscillations in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation ⋮ Bifurcation analysis of mixed-mode oscillations and Farey trees in an extended Bonhoeffer-van der Pol oscillator ⋮ Analysis of chaotic oscillations induced in two coupled Wilson-Cowan models ⋮ Nested mixed-mode oscillations in the forced van der Pol oscillator ⋮ Experimental and numerical study of the synchronization of canards in identical coupled canard-generating Bonhoeffer-van der Pol oscillators ⋮ Nested mixed-mode oscillations. III: Comparison of bifurcation structures between a driven Bonhoeffer-van der Pol oscillator and Nagumo-Sato piecewise-linear discontinuous one-dimensional map ⋮ Experimental and Numerical Observation of Successive Mixed-Mode Oscillation-Incrementing Bifurcations in an Extended Bonhoeffer–van der Pol Oscillator ⋮ Nested mixed-mode oscillations ⋮ Control of chaotic behavior in the dynamics of generalized Bonhoeffer-van der Pol system: effect of asymmetric parameter ⋮ Fractal structures in centrifugal flywheel governor system ⋮ Mixed-mode oscillation in a class of delayed feedback system and multistability dynamic response ⋮ Nested mixed-mode oscillations in a canard-generating driven Bonhoeffer-van der Pol oscillator ⋮ Mixed mode oscillations in the Bonhoeffer-van der Pol oscillator with weak periodic perturbation ⋮ Nested mixed-mode oscillations. II: Experimental and numerical study of a classical Bonhoeffer-van der Pol oscillator

Uses Software

• XPPAUT

Cites Work

• Period-doubling cascades of canards from the extended Bonhoeffer-van der Pol oscillator
• Resonance effects in the Bonhoeffer-van der Pol system.
• Multimodal oscillations in systems with strong contraction
• A Numerical Approach to Ergodic Problem of Dissipative Dynamical Systems
• Simulating, Analyzing, and Animating Dynamical Systems
• Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example
• Threshold, excitability and isochrones in the Bonhoeffer–van der Pol system
• Geometry of Mixed-Mode Oscillations in the 3-D Autocatalator

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