Permanence and almost periodic solution of two-species delayed Lotka–Volterra cooperative systems with impulsive perturbations

ABSTRACT

By applying the comparison theorem and the Lyapunov method of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution in a class of two-species Lotka–Volterra cooperative systems with impulses. The method used in this paper provides a possible method to study the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution of the models with impulsive perturbations in biological populations. Finally, an example and numerical simulations are given to illustrate that our results are feasible.

KEYWORDS:

• Comparison theorem
• cooperative system
• permanence
• almost periodicity
• impulse

MATHEMATICS SUBJECT CLASSIFICATION:

• 34K14
• 34K20
• 34K45
• 92D25