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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 periodic solutions in a higher order difference equation

Chuanxi Qian, Justin Smith (2018)

Archivum Mathematicum

Consider the following higher order difference equation x ( n + 1 ) = f ( n , x ( n ) ) + g ( n , x ( n - k ) ) , n = 0 , 1 , ⋯ where f ( n , x ) and g ( n , x ) : { 0 , 1 , ⋯ } × [ 0 , ∞ ) → [ 0 , ∞ ) are continuous functions in x and periodic functions in n with period p , and k is a nonnegative integer. We show the existence of a periodic solution { x ˜ ( n ) } under certain conditions, and then establish a sufficient condition for { x ˜ ( n ) } to be a global attractor of all nonnegative solutions of the equation. Applications to Riccati difference equation and some other difference equations derived from mathematical biology are also given.

Existence and global attractivity of positive almost periodic solutions for a kind of fishing model with pure-delay

Tianwei Zhang, Yongzhi Liao (2017)

Kybernetika

By using some analytical techniques, modified inequalities and Mawhin's continuation theorem of coincidence degree theory, some sufficient conditions for the existence of at least one positive almost periodic solution of a kind of fishing model with delay are obtained. Further, the global attractivity of the positive almost periodic solution of this model is also considered. Finally, three examples are given to illustrate the main results of this paper.

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.

Currently displaying 621 – 640 of 1850