Complex mixed-mode periodic and chaotic oscillations in a simple three-variable model of nonlinear system

DOI10.1063/1.166496zbMath0977.34038OpenAlexW1973814269WikidataQ73462890 ScholiaQ73462890MaRDI QIDQ4515153

Peter E. Strizhak, Vyacheslav O. Khavrus, A. L. Kawczyński

Publication date: 12 November 2000

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.166496

zbMATH Keywords

bifurcationsmixed-mode oscillationsBelousov-Zhabotinsky system

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28)

Related Items (11)

Bifurcation analysis of mixed-mode oscillations and Farey trees in an extended Bonhoeffer-van der Pol oscillator ⋮ 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 ⋮ Numerical Analysis of a Novel 3D Chaotic System with Period-Subtracting Structures ⋮ Nested mixed-mode oscillations in a canard-generating driven Bonhoeffer-van der Pol oscillator ⋮ Mixed-mode oscillations from a constrained extended Bonhoeffer–van der Pol oscillator with a diode ⋮ On decomposing mixed-mode oscillations and their return maps ⋮ Nested mixed-mode oscillations. II: Experimental and numerical study of a classical Bonhoeffer-van der Pol oscillator

Cites Work

• At the other side of a saddle-node
• Singular perturbation theory of traveling waves in excitable media (A review)
• Periodic orbits for interval maps with sharp cusps
• Varieties of spiral wave behavior: An experimentalist’s approach to the theory of excitable media
• Deterministic Nonperiodic Flow

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