Stochastic Nicholson’s blowflies delay differential equation with regime switching

Abstract

In this paper, we investigate the global existence of almost surely positive solution to a stochastic Nicholson's blowflies delay differential equation with regime switching, and give the estimation of the path. The results presented in this paper extend some corresponding results in Wang et al. Stochastic Nicholson's blowflies delayed differential equations, Appl. Math. Lett. 87 (2019) 20-26.

Stationary distribution and periodic solution of a stochastic Nicholson's blowflies model with distributed delay

“…To better observe such sudden environment switch to different states, we will consider the Markov chain into the Nicholson's blowflies model (2). Assume that there are N regimes and the switching between them on the state space S = {1, 2, ..., N}, 𝜉(t) be a continuous-time Markov chain with its generator Γ = (q i𝑗 ) N×N given by…”

“…Select the following parameter values in system ( 6) The only difference in Figure 2 is: 𝜎(1), 𝜎 (2) and 𝜎( 3) have different values. For the stochastic model ( 6) and its corresponding deterministic system, we observe that the Nicholson's blowflies X(t) will eventually die out, which is consistent with the result of Theorem 3.4 (see Figure 2).…”

“…A basic mathematical model has been widely adopted to describe the dynamics of Nicholson's blowflies (see Zhu et al 2 and Wang et al 3 ). The classic Nicholson's blowflies model is thought to be more practical by fitting the experimental data.…”

“…They studied the ultimate boundedness in the mean of a solution and estimated the sample Lyapunov exponent of the solution. The modified model for Nicholson's blowflies was described by Zhu et al 2 as follows: with initial conditions , for s ∈ [− τ , 0], ϕ ∈ C ([− τ , 0], [0, + ∞ )), ϕ (0) > 0. X ( t ) denotes the total number of Nicholson's blowflies at time t , δ represents the daily mortality rate of adult Nicholson's blowflies, p is the maximum daily spawning rate, τ is time of each generation, gives the maximum growth rate of reproduction of Lucilia cuprina, σ 2 is the white noise intensity.…”

“…According to the observation of the population, the time disturbance will affect the population system after a period of time, in essence, it is subject to the time delay of mature period from young population to adult population and the population reproduction cycle. [2][3][4] For instance, Huang proved the global asymptotic stability of zero equilibrium point for delay Nicholson's blowflies model. 4 Accordingly, it is of great significance to introduce time-delay into the biological mathematical model, which analyze the influence of time-delay on its dynamic characteristics.…”