Hassell-Varley Functional Response Research Articles

Dynamic behavior analysis of a feedback control predator-prey model with exponential fear effect and Hassell-Varley functional response

Considering that predator-induced fear effects affect the reproductive ability of the prey, as well as predator-predator interference during predation, a predator-prey model with exponential fear effect and Hassell-Varley functional response is proposed. The effects of fear level and the Hassell-Varley constant on the dynamics of the system are analyzed, and the results show that for predators that form tight groups, appropriately increasing the fear level can stabilize the system, while for other predators that do not form tight groups, the effect of fear on equilibrium stability is not particularly obvious. Besides, in order to reduce the negative impact of prey population on the environment, a feedback control strategy is applied to the system, and the existence and stability of order-n periodic solution are investigated by using the method of successive function, Poincaré map and Analogue to Poincaré criterion respectively. The periodic solution not only provides the conditions for control measures to be implemented, but also ensures that the prey population after control does not exceed a given level. To verify the correctness of the theoretical results obtained in this paper, numerical simulations for both models are carried out in MATLAB programs.

Stability and Bifurcation Analysis of Hassell–Varley Prey–Predator System with Fear Effect

In this work, we study a prey–predator system with Hassell–Varley functional response, which is a predator-dependent functional response. Our goal is to study the dynamics of the system in the presence of fear of predation risk. Hassell–Varley functional response is used when the predator population forms a fixed number of tight groups like for foraging purposes. Those predators can be terrestrial and aquatic. We assume that the birth rate of prey population reduces due to fear of the predator. Here, we have discussed the existence of biologically relevant equilibria and derived the condition for local asymptotic stability. Further, permanence and persistence are discussed to understand the dynamics of the system. The system undergoes Hopf bifurcation for both: the fear parameter f and interference coefficient $$\gamma $$ . Stability and the direction of Hopf bifurcation are also discussed. We observe that limit cycle oscillation can be prevented by increasing the cost of fear of the predator population. Numerical simulation is performed to substantiate our analytical findings.

Dynamic Properties of a Stochastic Predator-prey System with Hassell-Varley Functional Response

The dynamic properties of a stochastic predator-prey system with assell-Varley functional response is investigated in this paper. A Lyapunov function is established to analyze existence of the unique positive solution to the system for any positive initial value. We can draw a conclusion that the positive solution is stochastically bounded. At the end, some figures are presented to illustrate the main results.

Dynamical behaviours of an impulsive food-chain system with Hassell-Varley functional response and mutual interference

An impulsively controlled food-chain system with Hassell-Varley functional response and mutual interference is established in this paper. By applying theories and methods of ecology and ordinary differential equation, the dynamical complexity of this system is investigated. We give conditions of the extinction of prey and top predator and show that this system is uniformly bounded. By use of Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability and global stability of the prey-free and top predator-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent via impulsive comparison theorem. Finally, numerical simulations are given to substantiate our theoretical results and to illustrate various dynamical behaviours of this system.

Dynamical behaviours of an impulsive food-chain system with Hassell-Varley functional response and mutual interference

Dynamical behaviours of an impulsive food-chain system with Hassell-Varley functional response and mutual interference

一类具有季节效应的脉冲控制生物系统动力学研究

基于生态学理论与数学生物学知识，在动态建模过程中加入了Hassell-Varley功能反应函数，建立了一类具有季节效应的脉冲控制生物动力系统。借助脉冲微分方程的Floquet定理与比较定理，分析了系统半平凡周期解的存在性、局部渐近稳定性和全局渐近稳定性，同时讨论了系统生物种群的灭绝性与持久生存性。这些研究结果为进一步研究如何运用脉冲控制策略维持生态种群持久生存提供了一定的理论支撑。 In this paper, firstly, on the basis of ecology theory and mathematical biology knowledge, an impulsive controlled biological dynamical system with seasonal effect has been established by introducing Hassell-Varley functional response in the process of dynamic modeling. Secondly, using the Floquet theory and comparison theorem of impulsive differential equations, the existence, local asymptotic stability and global asymptotic stability of the semi-trivial periodic solution have been analyzed, and then the extinction and permanence of biological populations in the system have also been discussed. Finally, all those results can provide some theoretical support for further researching how to utilize control strategy to maintain the survival of ecological populations.

The dynamical complexity of a predator–prey system with Hassell–Varley functional response and impulsive effect

In this paper, the dynamics of an impulsively controlled predator–prey system with the Hassell–Varley functional response are studied. Under impulsive control, the conditions for the existence of a stable prey-free solution and for the permanence of the system are investigated by using Floquet theory and comparison theorems. Also the existence of a nontrivial periodic solution under some conditions is shown via the bifurcation theorem. Finally, numerical simulations are given to substantiate our theoretical results and to illustrate various dynamical behaviors of the system.