Global Behavior of Solutions in a Predator-Prey Cross-Diffusion Model with Cannibalism

Complexity 2020:1-19 (2020)

Abstract
The global asymptotic behavior of solutions in a cross-diffusive predator-prey model with cannibalism is studied in this paper. Firstly, the local stability of nonnegative equilibria for the weakly coupled reaction-diffusion model and strongly coupled cross-diffusion model is discussed. It is shown that the equilibria have the same stability properties for the corresponding ODE model and semilinear reaction-diffusion model, but under suitable conditions on reaction coefficients, cross-diffusion-driven Turing instability occurs. Secondly, the uniform boundedness and the global existence of solutions for the model with SKT-type cross-diffusion are investigated when the space dimension is one. Finally, the global stability of the positive equilibrium is established by constructing a Lyapunov function. The result indicates that, under certain conditions on reaction coefficients, the model has no nonconstant positive steady state if the diffusion matrix is positive definite and the self-diffusion coefficients are large enough.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1155/2020/1265798
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 49,128
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Analytics

Added to PP index
2020-05-23

Total views
1 ( #1,404,102 of 2,311,514 )

Recent downloads (6 months)
1 ( #753,566 of 2,311,514 )

How can I increase my downloads?

Downloads

Sorry, there are not enough data points to plot this chart.

My notes

Sign in to use this feature