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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Transversality for time-periodic competitive-cooperative tridiagonal systems

Pages: 1821 - 1830, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1821

 
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Yi Wang - Wu Wen-Tsun Key Laboratory, School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui, 230026, China (email)
Dun Zhou - Wu Wen-Tsun Key Laboratory, School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui, 230026, China (email)

Abstract: Transversality of the stable and unstable manifolds of hyperbolic periodic solutions is proved for tridiagonal competitive-cooperative time-periodic systems. We further show that such systems admit the Morse-Smale property provided that all the fixed points (of the corresponding Poincaré map) are hyperbolic. The main tools used here are the integer-valued Lyapunov function, as well as the Floquet theory developed in [1] for general time-dependent tridiagonal linear systems.

Keywords:  Transversality, competitive-cooperative systems, Floquet theory, hyperbolicity, Morse-Smale property.
Mathematics Subject Classification:  Primary: 37C20, 34D30, 92D25; Secondary: 37C25, 37C60.

Received: July 2014;      Revised: January 2015;      Available Online: June 2015.

 References