Diffusion driven instability and Hopf bifurcation in spatial predator-prey model on a circular domain

DOI10.1016/j.amc.2015.03.070zbMath1410.92092OpenAlexW2019292700WikidataQ115598304 ScholiaQ115598304MaRDI QIDQ1643065

Azgal Abichou, Habib Bouhafa, Radouane Yafia, Walid Abid, Moulay Aziz-Alaoui

Publication date: 18 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.03.070

zbMATH Keywords

chaospattern formationpredator-prey modeldisc domainHopf and Turing bifurcationLocal and global stability

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Population dynamics (general) (92D25)

Related Items

Turing Instability and Hopf Bifurcation in a Modified Leslie–Gower Predator–Prey Model with Cross-Diffusion ⋮ Dynamic complexity of a fractional-order predator-prey system with double delays ⋮ Spatiotemporal patterns induced by four mechanisms in a tussock sedge model with discrete time and space variables ⋮ Cross diffusion induced spatiotemporal pattern in diffusive nutrient-plankton model with nutrient recycling ⋮ Unnamed Item ⋮ Bifurcation, chaos and pattern formation in a space- and time-discrete predator-prey system ⋮ Complex patterns in a space-time discrete mathematical model of antibiotic resistance in hospitals with self-diffusion ⋮ Synchronization of Turing patterns in complex networks of reaction–diffusion systems set in distinct domains ⋮ Analysis of bifurcation, chaos and pattern formation in a discrete time and space Gierer Meinhardt system ⋮ A new finding on pattern self-organization along the route to chaos ⋮ Pattern dynamics in a Gierer-Meinhardt model with a saturating term ⋮ Dynamics of diffusive modified Previte-Hoffman food web model ⋮ Bifurcation, Chaos and Turing Instability Analysis for a Space-Time Discrete Toxic Phytoplankton-Zooplankton Model with Self-Diffusion ⋮ Spatiotemporal complexity of a discrete space-time predator-prey system with self- and cross-diffusion ⋮ Instability and Pattern Formation in Three-Species Food Chain Model via Holling Type II Functional Response on a Circular Domain

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of periodic travelling waves solutions in predator prey model with diffusion
• Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay
• Global dynamics of a predator-prey model
• Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
• Limit cycle and numerical similations for small and large delays in a predator-prey model with modified Leslie-Gower and Holling-type II schemes
• Study of a Leslie-Gower-type tritrophic population model
• Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• Should all the species of a food chain be counted to investigate the global dynamics?
• Spatiotemporal dynamics of reaction-diffusion models of interacting populations
• Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response
• Existence of traveling wave solutions in a diffusive predator-prey model
• Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations
• Persistence and global stability in a delayed Leslie-Gower type three species food chain
• Global bifurcation of co-existence states for a predator-prey-mutualist model with diffusion
• A survey of constructing Lyapunov functions for mathematical models in population biology
• Spatial pattern in a diffusive predator–prey model with sigmoid ratio-dependent functional response
• Global analyses in some delayed ratio-dependent predator-prey systems
• Analysis of the dynamics of a realistic ecological model