Dynamics of a two-dimensional slow-fast Belousov-Zhabotinsky model

DOI10.1007/s12346-024-01139-0MaRDI QIDQ6624359

Ruihan Xu, Ming Sun, Xiang Zhang

Publication date: 25 October 2024

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

global stabilityslow-fast systemsrelaxation oscillationcanard explosionBelousov-Zhabotinsky differential systems

Mathematics Subject Classification ID

Dynamical systems in biology (37N25) Bifurcation theory for ordinary differential equations (34C23) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Qualitative investigation and simulation of ordinary differential equation models (34C60) Global stability of solutions to ordinary differential equations (34D23) Dynamical aspects of attractors and their bifurcations (37G35) Stability theory for smooth dynamical systems (37C75) Systems with slow and fast motions for nonlinear problems in mechanics (70K70) Relaxation oscillations for ordinary differential equations (34C26) Canard solutions to ordinary differential equations (34E17)

Cites Work

• Unnamed Item
• Unnamed Item
• Belousov-Zhabotinsky type reactions: the non-linear behavior of chemical systems
• Geometric singular perturbation theory for ordinary differential equations
• Excitable neurons, firing threshold manifolds and canards
• Qualitative theory of planar differential systems
• Extending geometric singular perturbation theory to nonhyperbolic points -- fold and canard points in two dimensions
• HIDDEN ATTRACTORS IN DYNAMICAL SYSTEMS. FROM HIDDEN OSCILLATIONS IN HILBERT–KOLMOGOROV, AIZERMAN, AND KALMAN PROBLEMS TO HIDDEN CHAOTIC ATTRACTOR IN CHUA CIRCUITS
• Canard Induced Mixed-Mode Oscillations in a Medial Entorhinal Cortex Layer II Stellate Cell Model
• Canard Cycles
• Dynamics of the predator–prey model with the Sigmoid functional response
• Global Stability and Canard Explosions of the Predator-Prey Model with the Sigmoid Functional Response
• Relaxation oscillation and canard explosion
• On the limit cycle of a Belousov–Zhabotinsky differential systems

This page was built for publication: Dynamics of a two-dimensional slow-fast Belousov-Zhabotinsky model