Almost Periodic Solution of a Modified Leslie-Gower Predator-Prey Model with Beddington-DeAngelis Functional Response and Feedback Controls

Abstract EN

We consider a modified Leslie-Gower predator-prey model with the Beddington-DeAngelis functional response and feedback controls as follows: x ˙ t = x t a 1 t - b t x t - c t y t / α t + β t x t + γ t y t - e 1 t u t , u ˙ t = - d 1 t u t + p 1 t x t - τ , y ˙ t = y t a 2 t - r t y t / x t + k t - e 2 t ν t , and ν ˙ ( t ) = - d 2 ( t ) ν ( t ) + p 2 ( t ) y ( t - τ ) .

Sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.