Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

The aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

Analysis of a Stochastic Competitive Model with Distributed Time Delays and Jumps in a Polluted Environment

In this paper, a stochastic competitive model with distributed time delays and Lévy jumps is formulated. With or without a polluted environment, the model is denoted by (M) or (M0), respectively. The existence of positive solution, persistence in mean, and extinction of species for (M) and (M0) are both studied. The sufficient criteria of stability in distribution for model (M) is obtained. Finally, some numerical simulations are given to illustrate our theoretical results.

Dynamics and optimal harvesting of a stochastic predator-prey system with regime switching, S-type distributed time delays and Lévy jumps

<abstract><p>This work is concerned with a stochastic predator-prey system with S-type distributed time delays, regime switching and Lévy jumps. By use of the stochastic differential comparison theory and some inequality techniques, we study the extinction and persistence in the mean for each species, asymptotic stability in distribution and the optimal harvesting effort of the model. Then we present some simulation examples to illustrate the theoretical results and explore the effects of regime switching, distributed time delays and Lévy jumps on the dynamical behaviors, respectively.</p></abstract>

Synchronization stability on the BAM neural networks with mixed time delays

This article investigates the general decay synchronization (GDS) for the bidirectional associative memory neural networks (BAMNNs). Compared with previous research results, both time-varying delays and distributed time delays are taken into consideration. By using Lyapunov method and using useful inequality techniques, some sufficient conditions on the GDS for BAMNNs are derived. Finally, a numerical example is also carried out to validate the practicability and feasibility of our proposed results. It is worth pointing out that the GDS may be specialized as exponential synchronization, polynomial synchronization and logarithmic synchronization. Besides, we can estimate the convergence rate of the synchronization by GDS. The obtained results in this article can be seen as the improvement and extension of the previously known works.

Time-Delay Systems: An Overview

Time-delay naturally arises in many real-world systems, due to the fact that the instantaneous rate of change of such systems does not only depend on their current time but rather on their previous history as well. Hence, time-delays are ubiquitous, their introduction often leads to suppression of oscillations, multistability and chaotic motion in the dynamical systems. This review presents some models with different kinds of time-delays such as discrete, distributed and combination of both discrete and distributed time-delays with special emphasis on the reason of incorporating such delays into the system.