Dynamical Analysis of a Stochastic Predator-Prey System with Lévy Noise and Impulsive Toxicant Input

This paper established a modified Leslie-Gower and Holling-type IV stochastic predator-prey model with Lévy noise and impulsive toxicant input. We study the stability in distribution of solutions by inequality techniques and ergodic method. By comparison method and Itô’s formula, we obtain the sufficient conditions for the survival of each species. Some numerical simulations are introduced to show the theoretical results.

Global qualitative analysis of new Monod type chemostat model with delayed growth response and pulsed input in polluted environment

In this paper, we consider a new Monod type chemostat model with time delay and impulsive input concentration of the nutrient in a polluted environment. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ＂microorganism-extinction＂ periodic solution. Further, we establish the sufficient conditions for the global attractivity of the microorganism-extinction periodic solution. Using new computational techniques for impulsive and delayed differential equation, we prove that the system is permanent under appropriate conditions. Our results show that time delay is ＂profitless＂.

Modeling impulsive resource inputs in host-parasitoid interactions with time delays

For the interaction of parasitoids and their insect hosts in the laboratory environment, a novel mathematical model with impulsive resource inputs, stage-structure, maturation delays and negative binomial distribution is proposed. Based on the adaptability of the insect host to the environment, we study the permanence of the system in two cases and gain conditions under which the host and parasitoid species can coexist with impulsive resource inputs. We also discuss the existence of the positive periodic solution when the system is permanent by applying a fixed point theory. Besides, we perform numerical simulations which not only confirm but also further enhance our theoretical results. The simulations show that when total input of resource is fixed, smaller input amounts with shorter periods of impulsive delivery produce smaller oscillation amplitudes for both the host and parasitoid populations at the juvenile stage. However, both the densities of adult host and adult parasitoid are not affected by the resource management strategy. Furthermore, we also reconfirm that larger maturation delays, either the host or the parasitoid＇s delay, lead to any more individuals staying at the inmature stage of the species, while the adult populations decline dramatically at the same time. On the other hand, larger host maturation delays promote the parasitoid＇s population growth at both stages, and the impact of parasitoid maturation delay on the host population is almost the same but not as dramatic. These findings give us a deeper understanding about the host parasitoid interaction in laboratory environment.

Consensus of multi-agent systems with dynamic join characteristics under impulsive control

We study how to achieve the state consensus of a whole multi-agent system after adding some new agent groups dynamically in the original multi-agent system.We analyze the feasibility of dynamically adding agent groups under differen t forms of net work topologies that are currently common,and obtain four feasible schemes in theory,including one scheme that is the best in actual industrial production.Then,we carry out dynamic modeling of multi-agent systems for the best scheme.Impulsive control theory and Lyapunov stability theory are used to analyze the conditions so that the whole multi-agent system with dynamic join characteristics can achieve state consensus.Finally,we provide a numerical example to verify the practicality and validity of the theory.