Existence of traveling wave solutions in a singularly perturbed predator-prey equation with spatial diffusion
DOI10.3934/dcds.2023097zbMath1530.34052OpenAlexW4386452507MaRDI QIDQ6091070
Publication date: 23 November 2023
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcds.2023097
traveling wavegeometric singular perturbation theoryspatial diffusioncanard explosionperiodic wave train
Nonlinear boundary value problems for ordinary differential equations (34B15) Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Singular perturbations for ordinary differential equations (34E15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Relaxation oscillations for ordinary differential equations (34C26) Traveling wave solutions (35C07) Canard solutions to ordinary differential equations (34E17)
Cites Work
- Unnamed Item
- Canard limit cycles and global dynamics in a singularly perturbed predator-prey system with non-monotonic functional response
- A singular reaction-diffusion system modelling prey-predator interactions: invasion and co-extinction waves
- Relaxation oscillations and canard explosion in a predator-prey system of Holling and Leslie types
- Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey
- Traveling wave solutions for a predator-prey system with sigmoidal response function
- Existence of traveling wave solutions for diffusive predator-prey type systems
- A geometric approach in the study of traveling waves for some classes of non-monotone reaction-diffusion systems
- Geometric singular perturbation theory for ordinary differential equations
- Geometric singular perturbation theory analysis of an epidemic model with spontaneous human behavioral change
- More traveling waves in the Holling-Tanner model with weak diffusion
- The entry-exit theorem and relaxation oscillations in slow-fast planar systems
- Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion
- Traveling waves for a generalized Holling-Tanner predator-prey model
- Traveling waves in a diffusive predator-prey model with Holling type-III functional response
- Allee effect in a diffusive predator-prey system with nonlocal prey competition
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Extending slow manifolds near transcritical and pitchfork singularities
- Travelling Waves in Predator-Prey Systems
- Homoclinic bifurcations in slow-fast second order systems
- Relaxation Oscillations and the Entry-Exit Function in Multidimensional Slow-Fast Systems
- Dynamics of the predator–prey model with the Sigmoid functional response
- Relaxation oscillation and canard explosion
- The entry-exit function and geometric singular perturbation theory