Dynamics Of Predator-Prey System With Random Perturbations And Beddington-DeAngelis Functional Response

In population dynamics, with the functional response of predator - prey system has been cause for concern. Recently, some with Beddington-DeAngelis functional response model has been well studied. However, due to the traditional model of Beddington-DeAngelis lack of random white noise disturbance factor to consider in particular, therefore, further study of random interference with the Beddington-DeAngelis functional response of predator - prey system model is also significant.In this paper, a class of random perturbations of the Beddington-DeAngelis functional response of predatory behavior of the system dynamics, the main contents are:The first part of a class with Beddington-DeAngelis functional response of the random predator system Global Existence of Positive Solutions. First, a random white noise disturbance in the environment, the predator functional response with BD mathematical model of the system, and then using Lyapunov function method and the Ito formula, the assumption (A): a_i (t ) > 0 and bounded; b_i (t ),α(t ),β(t ),γ(t )bounded set up the circumstances, proof positive solution does not blow up in finite time, which is the global existence of positive solutions.The second part of the random disturbances with Beddington-DeAngelis functional response and prey systems exponential stability of positive solutions. On the assumption that (B): r_i ( t ), a_i ( t ), b_i ( t ),α( t ),β(t ),γ(t ) > 0( i= 1,2),and satisfy the matrix Negative definite conditions, then for any given initial value. Show that the system is stable for stochastic index.