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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.

Anti-periodic solutions for a higher order difference equation with p-Laplacian

Kong L., Parsley J., Rizzo K., Russell N.

Journal of Applied Analysis

2017

Vol. 23, nr 2

111--125

A higher order difference equation is studied. The equation is defined onℤand contains a p-Laplacian and both advance and retardation. Some criteria are established for the existence of infinitely many anti-periodic solutions of the equation. Several consequences of the main theorems are also included. Two examples are provided to illustrate the applicability of the 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