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Anti-periodic solutions for Clifford-valued high-order Hopfield neural networks with state-dependent and leakage delays

Huo Nina, Li Bing, Li Yongkun

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 1

83--98

A class of Clifford-valued high-order Hopfield neural networks (HHNNs) with state-dependent and leakage delays is considered. First, by using a continuation theorem of coincidence degree theory and the Wirtinger inequality, we obtain the existence of anti-periodic solutions of the networks considered. Then, by using the proof by contradiction, we obtain the global exponential stability of the anti-periodic solutions. Finally, two numerical examples are given to illustrate the feasibility of our results.

Four positive periodic solutions of a discrete time Lotka-Volterra competitive system with harvesting terms

Liu X., Ren Y., Li Y.

Opuscula Mathematica

2011

Vol. 31, no. 2

257-267

In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.

Existence and uniqueness of anti-periodic solutions for a class of nonlinear n-th order functional differential equations

Liu L., Li Y.

Opuscula Mathematica

2011

Vol. 31, no. 1

61-74

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

Zhang Q., Yang L., Liao D.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 4

649-658

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.

On the existence of positive periodic solutions of a delay logistic equation

Zhao C.-J., Wang K.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 2

155-160

In this paper, we discuss the existence of positive periodic solutions for a delay logistic equation, by using the theory of coincidence degree.