Abstract
The authors introduce stochasticity into a predator-prey system with Beddington-DeAngelis functional response and stage structure for predator. We present the global existence and positivity of the solution and give sufficient conditions for the global stability in probability of the system. Numerical simulations are introduced to support the main theoretical results.
Highlights
IntroductionIn [3], the authors studied the global properties of a predator-prey model with nonlinear functional response and stage structure for the predator, and the condition of the existence and the global stability of the positive steady states were established
The classical predator-prey model with BeddingtonDeAngelis type functional response can be denoted as ẋ (t) = x [b1 − a11x + a12y mx + ], ny (1) ẏ y [−b2
We discuss the biological significance of the model and establish sufficient conditions for global asymptotic stability of the model
Summary
In [3], the authors studied the global properties of a predator-prey model with nonlinear functional response and stage structure for the predator, and the condition of the existence and the global stability of the positive steady states were established. System (2) is greatly different from the model investigated in [3] for we comprehend that the effect of the response function will diminish the death rate of the predator and the predator does feed on the prey. If we take the environmental noise into account, we can replace the birth rate of prey population and death rate of predator population by an average value plus a random fluctuation, respectively, γ + σ (x − x∗) Ḃ (t) , d1 + σ1 (y1 − y1∗) Ḃ1 (t) ,.
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