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Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

Qianhong Zhang;  Lihui Yang;  Daixi Liao — 2011

International Journal of Applied Mathematics and Computer Science

Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

Existence and global attractivity of positive periodic solutions for a delayed competitive system with the effect of toxic substances and impulses

Changjin Xu;  Qianhong Zhang;  Maoxin Liao — 2013

Applications of Mathematics

In this paper, a class of non-autonomous delayed competitive systems with the effect of toxic substances and impulses is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least one positive periodic solution, and by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are established.

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