A-Stability of Global Attractors of Competition Diffusion Systems

作者：Hetzer Georg; Nguyen Tung; Shen Wenxian^*

来源：Journal of Dynamics and Differential Equations, 2010, 22(3): 533-561.

DOI：10.1007/s10884-010-9187-9

• Competition diffusion system
• Positive solution
• Semiflow
• Critical element
• Stable and unstable manifold
• Non-wandering point
• Global attractor
• Morse-Smale structure
• A-stability

We study the structural stability of global attractors (A-stability) for two-species competition diffusion systems with Morse-Smale structure. Such systems generate semiflows on positive cones of certain infinite-dimensionalBanach spaces (e.g., fractional order spaces). Our main result states that a two species competition diffusion system with Morse-Smale structure is structurally A-stable, which implies that the set of nonlinearities for which the system possesses Morse-Smale structure is open in an appropriate space under the topology of C(2)-convergence on compacta. Moreover, we provide a sufficient condition under which a system has Morse-Smale structure and provide some examples which satisfy the sufficient condition.

• 出版日期2010-9