A singular reaction-diffusion system modelling prey-predator interactions: invasion and co-extinction waves
From MaRDI portal
Publication:432439
DOI10.1016/j.jde.2012.04.005zbMath1258.35046OpenAlexW1988100702WikidataQ111492350 ScholiaQ111492350MaRDI QIDQ432439
Michel Langlais, Arnaut Ducrot
Publication date: 4 July 2012
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jde.2012.04.005
Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Ecology (92D40) Traveling wave solutions (35C07) Singular parabolic equations (35K67)
Related Items
Traveling wave solutions of a class of multi-species non-cooperative reaction–diffusion systems * ⋮ Bifurcation Analysis and Spatio-Temporal Patterns of a Prey–Predator Model with Hunting Cooperation ⋮ Traveling waves for a generalized Beddington-DeAngelis predator-prey model ⋮ Existence of positive periodic solutions for a neutral delay predator-prey model with Hassell-Varley type functional response and impulse ⋮ An effective iteration method for a class of nonlinear singular perturbed problems ⋮ Traveling wave solutions for a continuous and discrete diffusive predator-prey model ⋮ Boundary layer analysis of nonlinear reaction-diffusion equations in a polygonal domain ⋮ Traveling wave solutions of a diffusive ratio-dependent Holling-Tanner system with distributed delay ⋮ Bistability induced by generalist natural enemies can reverse pest invasions ⋮ Traveling waves for a generalized Holling-Tanner predator-prey model ⋮ Stabilization to a positive equilibrium for some reaction-diffusion systems ⋮ Sharp profiles in models of collective movements ⋮ Analytical detection of stationary turing pattern in a predator-prey system with generalist predator ⋮ Existence of traveling wave solutions in a singularly perturbed predator-prey equation with spatial diffusion ⋮ Analytical detection of stationary and dynamic patterns in a prey-predator model with reproductive Allee effect in prey growth ⋮ Traveling waves for a reaction-diffusion-advection predator-prey model ⋮ Behaviors of solutions for a singular prey-predator model and its shadow system ⋮ Traveling wave solutions of a nonlocal dispersal predator-prey model with spatiotemporal delay ⋮ Boundary layer analysis of nonlinear reaction-diffusion equations in a smooth domain ⋮ Hopf bifurcations and oscillatory patterns of a homogeneous reaction-diffusion singular predator-prey model ⋮ Recent developments on a singular predator-prey model ⋮ Global multiplicity for very-singular elliptic problems with vanishing non-local terms
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Existence and uniqueness of a sharp travelling wave in degenerate non- linear diffusion Fisher-KPP equations
- Nonsharp travelling wave fronts in the Fisher equation with degenerate nonlinear diffusion
- Travelling waves in nonlinear diffusion-convection reaction
- Travelling wave phenomena in some degenerate reaction-diffusion equations
- Qualitative analysis and travelling wave solutions for the SI model with vertical transmission
- Some remarks on a singular reaction-diffusion system arising in predator-prey modeling
- Quenching and propagation in KPP reaction-diffusion equations with a heat loss
- On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion
- The Formation of the Dead Core in Parabolic Reaction-Diffusion Problems
- Traveling Wave Solution for Some Nonlinear Diffusion Equations
- Modelling Biological Populations in Space and Time
- On the blow-up of solutions of a convective reaction diffusion equation
- Travelling waves in a nonlinear degenerate diffusion model for bacterial pattern formation