Relaxation Oscillations and the Entry-Exit Function in Multidimensional Slow-Fast Systems
From MaRDI portal
Publication:5003326
DOI10.1137/19M1295507zbMath1471.34082arXiv1910.06318OpenAlexW3176541892MaRDI QIDQ5003326
Publication date: 21 July 2021
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1910.06318
turning pointslow-fast systementry-exit functiongeometric singular perturbation theoryrelaxation oscillationdelay of stability loss
Population dynamics (general) (92D25) Singular perturbations for ordinary differential equations (34E15) Relaxation oscillations for ordinary differential equations (34C26)
Related Items (3)
Coexistence of one predator and two prey through rapid evolution in predator's feeding choice ⋮ Relaxation oscillations in slow–fast IS–LM economic models ⋮ Existence of traveling wave solutions in a singularly perturbed predator-prey equation with spatial diffusion
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Viscous singular shock profiles for a system of conservation laws modeling two-phase flow
- Multiple time scale dynamics
- Cyclicity of common slow-fast cycles
- Canard cycles for predator-prey systems with Holling types of functional response
- On bifurcation delay: an alternative approach using geometric singular perturbation theory
- The canard unchained or how fast/slow dynamical systems bifurcate
- Exchange lemmas 2: General exchange Lemma
- Sudden shifts in ecological systems: intermittency and transients in the coupled Ricker population model
- Relaxation oscillation profile of limit cycle in predator-prey system
- Generalized exchange lemmas and orbits heteroclinic to invariant manifolds
- Geometric singular perturbation theory for ordinary differential equations
- Limit cycles in slow-fast forest-pest models
- On Bendixson's criterion
- Exchange lemmas for singular perturbation problems with certain turning points
- Inferring parameters of prey switching in a 1 predator-2 prey plankton system with a linear preference tradeoff
- Composite waves in the Dafermos regularization
- Relaxation oscillations in a class of predator-prey systems.
- Relaxation oscillations in \({\mathbb R}^3\)
- Existence of Dafermos profiles for singular shocks
- Fast-slow dynamics for intraguild predation models with evolutionary effects
- A geometric analysis of the SIR, SIRS and SIRWS epidemiological models
- A criterion for the existence of relaxation oscillations with applications to predator-prey systems and an epidemic model
- The entry-exit theorem and relaxation oscillations in slow-fast planar systems
- The effects of predator evolution and genetic variation on predator-prey population-level dynamics
- Smoothness of transition maps in singular perturbation problems with one fast variable
- Slow-fast dynamics and nonlinear oscillations in transmission of mosquito-borne diseases
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Turning Points And Relaxation Oscillation Cycles in Simple Epidemic Models
- Existence of Chapman--Jouguet Detonation and Deflagration Waves
- Prey Switching with a Linear Preference Trade-Off
- A Predator--2 Prey Fast--Slow Dynamical System for Rapid Predator Evolution
- Shadowing Lemma and Singularly Perturbed Boundary Value Problems
- Invariant Manifolds and Singularly Perturbed Boundary Value Problems
- Stability Loss Delay and Smoothness of the Return Map in Slow-Fast Systems
- Predator–prey systems with small predator's death rate
- Number and Stability of Relaxation Oscillations for Predator-Prey Systems with Small Death Rates
- Canard cycles and center manifolds
- Geometric Singular Perturbation Theory Beyond the Standard Form
- Travelling waves in the Holling–Tanner model with weak diffusion
- Singular Perturbation Analysis of a Regularized MEMS Model
- Scaling in Singular Perturbation Problems: Blowing Up a Relaxation Oscillator
- Travelling waves for a thin liquid film with surfactant on an inclined plane
- Relaxation oscillation and canard explosion
- The entry-exit function and geometric singular perturbation theory
This page was built for publication: Relaxation Oscillations and the Entry-Exit Function in Multidimensional Slow-Fast Systems
