Abstract
This paper is concerned with a delay Lotka-Volterra model under regime switching diffusion in random environment. By using generalized Itô formula, Gronwall inequality and Young’s inequality, some sufficient conditions for existence of global positive solutions and stochastically ultimate boundedness are obtained, respectively. Finally, an example is given to illustrate the main results.
Highlights
The delay differential equation dx (t) dt = x (t) (a − bx (t) + cx (t τ)) (1)has been used to model the population growth of certain species and is known as the delay Lotka-Volterra model or the delay logistic equation
This work is concerned with delay Lotka-Volterra model under regime switching diffusion in random environment
Similar results are technically obtained by making use of comparison principle
Summary
Has been used to model the population growth of certain species and is known as the delay Lotka-Volterra model or the delay logistic equation. The switching between different environments is memoryless and the waiting time for the switch has an exponential distribution This indicates that we may model the random environments and other random factors in the system by a continuoustime Markov chain r(t), t ≥ 0 with a finite state space S = {1, 2, . The stochastic permanence and extinction of a logistic model under regime switching were considered in [20, 24], asymptotic results of a competitive Lotka-Volterra model in random environment are obtain in [25], a new single-species model disturbed by both white noise and colored noise in a polluted environment was developed and analyzed in [26], and a general stochastic logistic system under regime switching was proposed and was treated in [27]. An example and its numerical simulation are given to illustrate our main results
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