Abstract
In this paper, we are concerned with a non-autonomous competing model with time delays and feedback controls. Applying the comparison theorem of differential equations and by constructing a suitable Lyapunov functional, some sufficient conditions which guarantee the existence of a unique globally asymptotically stable nonnegative almost periodic solution of the system are established. An example with its numerical simulations is given to illustrate the feasibility of our results.
Highlights
In recent years, the competitive prey-predator systems have been investigated by many scholars
Sarwardi et al [27] focused on the local and the global stability and the bifurcations of a competitive preypredator system with a prey refuge, Ko and Ahn [16] discussed the global attractor, persistence and the stability of all non-negative equilibria of a diffusive one-prey and two-competing-predator system with a ratio-dependent functional response, Pan et al [25] considered Gause,s principle in interspecific competition of the cyclic predatorprey system, Qun Liu et al [23] addressed the global stability of a stochastic predatorprey system with infinite delays
The main object of this paper is to investigate the almost periodic solutions of model (2)
Summary
The competitive prey-predator systems have been investigated by many scholars. Theorem 3.2: If (H1)–(H3) hold, there exists a unique globally asymptotically stable nonnegative almost periodic solution of systems (2). Proof: By (3) and Lemma 2.4, there exists a bounded positive solution z(t) of system (2), t ≥ 0. − b1(t)κ1(t) − c1(t) − d1(t)ν1(t − τ1(t)) This proves that z(t) satisfies system (2) and z(t) is a nonnegative almost periodic solution, by Theorem 3.1, it follows that there exists a unique globally asymptotically stable nonnegative almost periodic solution of system (2).
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