Spatial pattern formation in ratio-dependent model: higher-order stability analysis

Math Med Biol. 2011 Jun;28(2):111-28. doi: 10.1093/imammb/dqq024. Epub 2010 Dec 6.

Abstract

The article presents a study of the spatiotemporal pattern formation in a Holling-Tanner prey-predator model with ratio-dependent functional response. Conditions for Turing bifurcation are obtained and different spatially inhomogeneous stationary patterns exhibited by the model system are presented. Then, reported patterns are the outcome of numerical simulation. The conditions for instability of inhomogeneous spatiotemporal perturbation around temporal steady state beyond the linear regime fall out from the analysis of higher-order perturbation terms. The analytical findings are validated with the numerical simulation results.

MeSH terms

  • Animals
  • Computer Simulation
  • Ecosystem*
  • Models, Biological*
  • Population Dynamics
  • Predatory Behavior*