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This article is concerned with a life energy system dynamic model with two different delays. A set of sufficient criteria which ensures the local stability and the existence of Hopf bifurcation for the model is derived. Some explicit formulas which determine the nature of Hopf bifurcations are obtained by means of the normal form theory and center manifold theorem. Our analytical findings are supported by numerical experiments. Finally, a brief conclusion is included. [ABSTRACT FROM AUTHOR]

This article concerns Liénard-type systems with time-varying de-lays. By applying the theory of exponential dichotomies, the properties of pseudo almost periodic function, inequality analysis techniques, and contrac tion mapping principle, new criteria for the existence and uniqueness of pseudo almost periodic solutions are established. An example is given to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

A periodic discrete time three species competition system is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous nonautonomous three species competition system is proposed. By using Gaines and Mawhin's continuation theoremof coincidence degree theory, sufficient conditions for the existence of positive periodic solutions of the model are obtained. [ABSTRACT FROM AUTHOR]

By using Schaeffer's theorem and Lyapunov functional, sufficient conditions of the existence and globally exponential stability of positive periodic solution to an impulsive neural network with time-varying delays are established. Applications, examples, and numerical analysis are given to illustrate the effectiveness of the main results. [ABSTRACT FROM AUTHOR]