Pattern formation in a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth
type: Item
instance of: scholarly article
title: Pattern formation in a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth
zbMATH Open document ID: 1264.34169
DOI: 10.1155/2013/454209
author: Bo Yang
published in: Discrete Dynamics in Nature and Society
publication date: 2013-06-13T00:00:00Z
review text: Summary: The spatiotemporal dynamics of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth subject to zero-flux boundary condition are investigated analytically and numerically. The asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation around the positive equilibrium are shown; the conditions of Turing instability are obtained. And with the help of numerical simulations, it is found that the model exhibits complex pattern replication: stripes, spots-stripes mixtures, and spots Turing patterns.
Mathematics Subject Classification ID: 34K60
Mathematics Subject Classification ID: 34K18
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6175084
zbMATH Keywords: positive equilibrium
zbMATH Keywords: asymptotic stability
zbMATH Keywords: diffusive ratio-dependent Holling-Tanner predator-prey model
Wikidata QID: Q58921599
describes a project that uses: PRED_PREY
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/454209
OpenAlex ID: W2067808676
cites work: A minimal model of pattern formation in a prey-predator system
cites work: The chemical basis of morphogenesis
cites work: Spatiotemporal Complexity of Plankton and Fish Dynamics
cites work: Mathematical biology. Vol. 2: Spatial models and biomedical applications.
cites work: Complex patterns in a predator-prey model with self and cross-diffusion
cites work: Spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge
cites work: Dynamical analysis of a delayed reaction-diffusion predator-prey system
cites work: Dynamics of a diffusive predator-prey model with additive Allee effect
cites work: Pattern formation in a cross-diffusive Holling-Tanner model
cites work: Dynamical analysis of a delayed ratio-dependent Holling-Tanner predator-prey model
cites work: Qualitative analysis of a ratio-dependent Holling-Tanner model
cites work: Turing instabilities and spatio-temporal chaos in ratio-dependent Holling-Tanner model
cites work: Q5675177
cites work: Environmental periodicity and time delays in a ``food-limited'' population model
cites work: On diffusive population models with toxicants and time delays
cites work: Periodicity in a ``food-limited'' population model with toxicants and time delays
cites work: Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB
cites work: PATTERN FORMATION IN NOISY SELF-REPLICATING SPOTS
Recommended article: Pattern formation in a ratio-dependent predator-prey model with cross-diffusion
Recommended article: Pattern formation in a semi-ratio-dependent predator-prey system with diffusion
Recommended article: Pattern formation in a cross-diffusive ratio-dependent predator-prey model
Recommended article: Q5475676
Recommended article: PATTERN FORMATION FOR A RATIO-DEPENDENT PREDATOR-PREY MODEL WITH CROSS DIFFUSION
Recommended article: Q3507191
Recommended article: Patterns formations in a diffusive ratio-dependent predator-prey model of interacting populations
Recommended article: Qualitative analysis of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth
Recommended article: Q3572175
Recommended article: Pattern formation in a predator-prey diffusion model with stage structure for the predator
description: scientific article; zbMATH DE number 6175084