Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System

DOI10.1142/S0218127417300257zbMath1370.34087MaRDI QIDQ5357139

K. Thamilmaran, S. Leo Kingston

Publication date: 14 September 2017

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

Liénard systemmixed-mode oscillationsbursting oscillationsmultistability and electronic circuit

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Analytic circuit theory (94C05) Qualitative investigation and simulation of ordinary differential equation models (34C60) Complex behavior and chaotic systems of ordinary differential equations (34C28) Nonautonomous smooth dynamical systems (37C60) Relaxation oscillations for ordinary differential equations (34C26)

Related Items (12)

The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction ⋮ Bifurcation analysis of mixed-mode oscillations and Farey trees in an extended Bonhoeffer-van der Pol oscillator ⋮ Bursting oscillations of the perturbed quasi-zero stiffness system with positive/negative stiffness at origin ⋮ 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 ⋮ A simple jerk-like system without equilibrium: asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees ⋮ Parametric excitation induced extreme events in MEMS and Liénard oscillator ⋮ Mixed-mode oscillation in a class of delayed feedback system and multistability dynamic response ⋮ Complex Bursting Patterns in a van der Pol–Mathieu–Duffing Oscillator ⋮ A memristor-meminductor-based chaotic system with abundant dynamical behaviors ⋮ Nested mixed-mode oscillations in a canard-generating driven Bonhoeffer-van der Pol oscillator ⋮ Dynamic mechanism of multiple bursting patterns in a whole-cell multiscale model with calcium oscillations ⋮ Complex mixed-mode oscillations based on a modified Rayleigh-Duffing oscillator driven by low-frequency excitations

Uses Software

• XPPAUT

Cites Work

• Control of multistability
• Bursting oscillations in Duffing's equation with slowly changing external forcing
• Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle
• Bifurcations of mixed-mode oscillations in a three-variable autonomous Van der Pol-Duffing model with a cross-shaped phase diagram
• Bifurcation of limit cycles and separatrix loops in singular Liénard systems
• Complex mixed-mode oscillations in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation
• An experimental study of slow passage through Hopf and pitchfork bifurcations in a parametrically driven nonlinear oscillator
• Mixed mode oscillations as a mechanism for pseudo-plateau bursting
• Symmetric Fold/Super-Hopf Bursting, Chaos and Mixed-Mode Oscillations in Pernarowski Model of Pancreatic Beta-Cells
• A NOTE ON PERIODIC SOLUTIONS OF A FORCED LIÉNARD-TYPE EQUATION
• Simulating, Analyzing, and Animating Dynamical Systems
• MULTISTABILITY AND RARE ATTRACTORS IN VAN DER POL–DUFFING OSCILLATOR
• BURSTING NEAR HOMOCLINIC BIFURCATION IN TWO COUPLED CHUA OSCILLATORS
• Inverse period-doubling bifurcations determine complex structure of bursting in a one-dimensional non-autonomous map
• Extreme multistability: Attractor manipulation and robustness
• Geometry of Mixed-Mode Oscillations in the 3-D Autocatalator
• Mixed-mode oscillations and slow manifolds in the self-coupled FitzHugh-Nagumo system

This page was built for publication: Bursting Oscillations and Mixed-Mode Oscillations in Driven Liénard System