Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays

Abstract

This paper proposes a stochastic three species food-chain model with harvesting and distributed delays. Some criteria for the global dynamics of all positive solutions, including the existence of global positive solutions, stochastic boundedness, extinction, global asymptotic stability in the mean, and the probability distribution, are established by using the stochastic integral inequalities, Lyapunov function method, and the inequality estimation technique. Furthermore, the effects of harvesting are discussed, the optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY for short) are obtained. Finally, numerical examples are carried out to illustrate our main results.

Dynamic analysis of a stochastic four species food-chain model with harvesting and distributed delay

“…Proof The proof of Lemma 4 is similar to Lemma 3 given in [28]. But, here we will give an improvement.…”

“…The sustainable maximum yield and optimal harvesting effort are also given. In [28], taking harvesting and distributed delays into consideration, the authors investigated a class of stochastic three species food-chain models. The global dynamics of the model, including global asymptotic stability, extinction, random boundedness, and the probability distribution are obtained.…”

Global dynamics and optimal harvesting in a stochastic two-predators one-prey system with distributed delays and Lévy noise

“…This completes the proof. Proof: Assume i > 0, then from (20) and (31), and the arbitrariness of ε we directly obtain lim sup…”

“…To investigate the optimal harvesting problem of model (2), we further introduce the following assumption and the asymptotic stability in the distribution for model (2). This lemma can be proved easily by using a standard argument as in [31,32]. Hence, we here omit it.…”

Finite time synchronization of stochastic Markovian jumping genetic oscillator networks with time-varying delay and Lévy noise

“…Note that the real cellular life is finite, so it should be more meaningful for considering finite-time synchronization in GONs. Although deterministic differential equations can capture some mean-field characteristics of practical dynamic systems, stochastic differential equations are more important in modeling uncertainties inherent in real world [24][25][26][27][28]. Gene expression is an intrinsically stochastic process [29,30].…”