Authors: Meng Hu
Addresses: School of Mathematics and Statistics, Anyang Normal University, Xian'ge Avenue 436, Anyang, Henan 455000, China
Abstract: This paper is concerned with an almost population dynamic system on time scales. Using the theory of calculus on time scales and some mathematical methods, several comparison theorems on time scales are established. Based on these results, we derive some sufficient conditions for permanence of the system. Moreover, using the properties of almost periodic functions and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of uniformly, asymptotically stable almost periodic solution of the system are obtained. As an application, we applying the obtained results to a single-species system with distributed delay on time scales. Finally, two examples together with their numerical simulations are presented to illustrate the feasibility and effectiveness of the results.
Keywords: almost periodic solutions; asymptotic stability; permanence; time scales; population dynamics; Lyapunov functional; single-species systems; numerical simulation.
International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.4, pp.318 - 334
Received: 02 Apr 2016
Accepted: 02 May 2016
Published online: 25 Jan 2017 *