Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 420386, 8 pages
http://dx.doi.org/10.1155/2014/420386
Research Article

Attractor for a Reaction-Diffusion System Modeling Cancer Network

Institute of Applied Mathematics, Xuchang University, Xuchang, Henan 461000, China

Received 12 January 2014; Accepted 26 March 2014; Published 17 April 2014

Academic Editor: Imran Naeem

Copyright © 2014 Xueyong Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain . Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in and prove that the solution converges to stable steady states. These results can help to understand the dynamical character of cancer network and propose a new insight to study the mechanism of cancer. In the end, the numerical simulation shows that the analytical results agree with numerical simulation.