# American Institute of Mathematical Sciences

August  2015, 20(6): 1821-1830. doi: 10.3934/dcdsb.2015.20.1821

## Transversality for time-periodic competitive-cooperative tridiagonal systems

 1 Wu Wen-Tsun Key Laboratory, School of Mathematical Science, University of Science and Technology of China, Hefei, Anhui, 230026, China, China

Received  July 2014 Revised  January 2015 Published  June 2015

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.
Citation: Yi Wang, Dun Zhou. Transversality for time-periodic competitive-cooperative tridiagonal systems. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1821-1830. doi: 10.3934/dcdsb.2015.20.1821
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