Stationary distribution of stochastic population systems under regime switching

On stochastic Gilpin–Ayala population model with Markovian switching

“…Moreover, they demonstrated that the solution is stochastically ultimately bounded and the time average of the second moment of the solution is also bounded. Very recently, Settati and Lahrouz (2014) have investigated the positive recurrence of an n-species model of facultative mutualism under regime switching system. Li et al (2009) discussed the stochastic permanence and extinction of a Lotka-Volterra system under regime switching, and they gave an estimation of the limit of the average in time of the sample path.…”

Periodic solution and stationary distribution of stochastic SIR epidemic models with higher order perturbation

“…This method has been utilized by many authors (see e.g. [18,20,21]). Studying such problem is meaningful and challenging.…”

“…The switching between environmental regimes is often memoryless and the waiting time for the next switching follows the exponential distribution [18]. Hence the regime switching can be modeled by a continuous time Markov chain (r(t)) t≥0 taking values in a finite state space.…”

Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input

“…Lemma 12 (see [77]). System (7) Moreover, the Markov process ( ( ), ( )) has a unique ergodic stationary distribution (⋅, ⋅).…”

“…Furthermore, the prey-predator model may be perturbed by telegraph noise which is distinguished by factors such as rain falls and nutrition and can be represented by switching among two or more regimes of environment [40,60,[70][71][72][73][74][75][76][77][78][79][80]. For example, population growth rates in different seasons are not the same.…”