Pattern Formation in a Diffusive Ratio-Dependent Holling-Tanner Predator-Prey Model with Smith Growth

Abstract

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.

Hopf Bifurcation Analysis for a Semiratio-Dependent Predator-Prey System with Two Delays

“…Numerous laboratory experiment, and observations have shown that a more suitable general predator-prey system should be based on the "ratio-dependent" theory, especially when predators have to search, share, or compete for food [1][2][3]. And ratiodependent predator-prey systems have been investigated by many scholars [4][5][6][7][8][9][10][11]. In [4], Zhang and Lu considered the following semi-ratio-dependent predator-prey system with the nonmonotonic functional response…”