All Possible Bursting Attractors in the Neighborhood of Hopf Bifurcation Point Under Periodic Excitation
DOI10.1142/S0218127422500791zbMath1502.34064MaRDI QIDQ5083098
Xiaofang Zhang, Yibo Xia, Qinsheng Bi, Junting Gou
Publication date: 21 June 2022
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Attractors of solutions to ordinary differential equations (34D45) Singular perturbations for ordinary differential equations (34E15) Nonautonomous smooth dynamical systems (37C60) Relaxation oscillations for ordinary differential equations (34C26)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bifurcation mechanism of bursting oscillations in parametrically excited dynamical system
- Bursting oscillations in Duffing's equation with slowly changing external forcing
- Geometric singular perturbation theory for ordinary differential equations
- Differential equations with small parameters and relaxation oscillations. Translation from the Russian by F. M. C. Goodspeed
- Matched asymptotic expansions. Ideas and techniques
- Symbolic computation of normal forms for semi-simple cases
- A hierarchy of transitions to mixed mode oscillations in an electrochemical system
- Topological and phenomenological classification of bursting oscillations
- Nonstandard analysis in practice
- Multiple scale and singular perturbation methods
- Complex mixed-mode oscillations in a Bonhoeffer-van der Pol oscillator under weak periodic perturbation
- Dynamics analysis of the fast-slow hydro-turbine governing system with different time-scale coupling
- Routes to bursting in a periodically driven oscillator
- Multi-timescale systems and fast-slow analysis
- Slow variable dominance and phase resetting in phantom bursting
- Numerically induced bursting in a set of coupled neuronal oscillators
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Extending slow manifolds near transcritical and pitchfork singularities
- Mixed-Mode Oscillations with Multiple Time Scales
- Mixed-Mode Oscillations in Three Time-Scale Systems: A Prototypical Example
- Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron
- NEURAL EXCITABILITY, SPIKING AND BURSTING
- Invariant manifolds
