This paper concerns delay differential systems that can be regarded as a model of two-neuron artificial neural network with delayed feedback. Some interesting results are obtained for the existence of a periodic solution for the system. Our approach is based on the continuation theorem of coincidence degree, and a-priori estimates of the periodic solutions.

In this paper, periodic solution of impulsive Lotka-Volterra recurrent neural networks with delays is studied. Using the continuation theorem of coincidence degree theory and analysis techniques, we establish criteria for the existence of periodic solution of impulsive Lotka-Volterra recurrent neural networks with delays.

In this paper, a Hopfield neural network with neutral time-varying delays is investigated by using the continuation theorem of Mawhin’s coincidence degree theory and some analysis technique. Without assuming the continuous differentiability of time-varying delays, sufficient conditions for the existence of the periodic solutions are given. The result of this paper is new and extends previous kn...

Abstract. In this paper, by using a continuation theorem of coincidence degree theory and a differential inequality, we establish some sufficient conditions ensuring the existence and global exponential stability of anti-periodic solutions for a class of fuzzy Cohen–Grossberg neural networks with time-varying and distributed delays. In addition, we present an illustrative example to show the fe...

This paper considers the existence of positive almost-periodic solutions for almost-periodic LotkaVolterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

In this paper, by using Mawhin’s continuation theorem of coincidence degree theory, we obtain some sufficient conditions for the existence of homoclinic solutions for a class of nonlinear second-order differential equations with timevarying delays. Moreover, we give an example to illustrate the feasibility of obtained results. Our results are completely new.

A delayed predator-prey system with prey dispersal in n-patch environments and impulse effects is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions to the system.

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.

A predator-prey system was studied that has a discrete delay, stage-structure, and Beddington-DeAngelis functional response, where predator species has three stages, immature, mature, and old age stages. By using of Mawhin's continuous theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution.

In this paper, we study a periodic ratio-dependent predator-prey system of two species with impulse and multiple time delays. By means of analysis techniques and the continuation theorem of coincidence degree theory, we obtain sufficient conditions for the existence of positive periodic solutions of the system. Our results extend previous results obtained in [9].