Turing bifurcation in a diffusive predator-prey model with schooling behavior. (English) Zbl 1423.92219
Summary: This paper mainly deals with the dynamics of a diffusive predator-prey model with schooling behavior. We firstly investigate the local stability of the interior equilibrium with the associated characteristic equation. Secondly, regarding the consumption rate \(\beta\) as the bifurcation parameter to study, the Turing bifurcations near \(E^\ast\). Besides, we study the stability and direction of the Turing bifurcations with the use of center manifold and canonical form theory. Finally, computer simulations are performed to illustrate our analytical findings, and the biological effect is discussed in the result.
MSC:
| 92D25 | Population dynamics (general) |
| 34C23 | Bifurcation theory for ordinary differential equations |
References:
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