Inhomogeneous spatial patterns in diffusive predator-prey system with spatial memory and predator-taxis

by   Yehu Lv, et al.

In this paper, we consider a diffusive predator-prey system with spatial memory and predator-taxis. Since in this system, the memory delay appears in the diffusion term, and the diffusion term is nonlinear, the classical normal form of Hopf bifurcation in the reaction-diffusion system with delay can't be applied to this system. Thus, in this paper, we first derive an algorithm for calculating the normal form of Hopf bifurcation in this system. Then in order to illustrate the effectiveness of our newly developed algorithm, we consider the diffusive Holling-Tanner model with spatial memory and predator-taxis. The stability and Hopf bifurcation analysis of this model are investigated, and the direction and stability of Hopf bifurcation periodic solution are also researched by using our newly developed algorithm for calculating the normal form of Hopf bifurcation. At last, we carry out some numerical simulations, two stable spatially inhomogeneous periodic solutions corresponding to the mode-1 and mode-2 Hopf bifurcations are found, which verifies our theoretical analysis results.



There are no comments yet.


page 20

page 21

page 22

page 23


Analysis of Flux Corrected Transport Schemes for Evolutionary Convection-Diffusion-Reaction Equations

We report in this paper the analysis for the linear and nonlinear versio...

A Chebyshev multidomain adaptive mesh method for Reaction-Diffusion equations

Reaction-Diffusion equations can present solutions in the form of travel...

A stability preserved time-integration method for nonlinear advection-diffusion models

A new implicit-explicit local differential transform method (IELDTM) is ...

A dual adaptive explicit time integration algorithm for efficiently solving the cardiac monodomain equation

The monodomain model is widely used in in-silico cardiology to describe ...

Pattern formation in a cell migration model with aggregation and diffusion

In this paper, we study pattern formations in an aggregation and diffusi...

Fast stable finite difference schemes for nonlinear cross-diffusion

The dynamics of cross-diffusion models leads to a high computational com...

Spatial and color hallucinations in a mathematical model of primary visual cortex

We study a simplified model of the representation of colors in the prima...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.