Hassell-Varley Type Functional Response Research Articles

Habitat complexity of a discrete predator-prey model with Hassell-Varley type functional response

Prey-predator models with a refuge effect are particularly significant in ecology. The two common conceptions of refuge in the literature are continual refuge and refuge pro-portionate to prey. Academics are already paying attention to new types of refuge concepts. Prey-predator interaction has become a prominent issue in recent biomathe-matical studies due to its environmental influence. In this paper, the habitat complexity of a predator-prey model with Hassell-Varley type functional response is considered. For this, we focused our study on the question of existence and uniqueness in Sec. 2. And Sec. 3 is devoted to show a generalized stability. Note that this representation also al-lows us to generalize the results obtained recently in the literature. In Sec. 4, we have studied the numerical algorithm for the suggested problem. The paper is ended by two examples illustrating our results.

Influence of Spatial Dispersal among Species in a Prey–Predator Model with Miniature Predator Groups

Dispersal among species is an important factor that can govern the prey–predator model’s dynamics and cause a variety of spatial structures on a geographical scale. These structures form when passive diffusion interacts with the reaction part of the reaction–diffusion system in such a way that even if the reaction lacks symmetry-breaking capabilities, diffusion can destabilize the symmetry and allow the system to have them. In this article, we look at how dispersal affects the prey–predator model with a Hassell–Varley-type functional response when predators do not form tight groups. By considering linear stability, the temporal stability of the model and the conditions for Hopf bifurcation at feasible equilibrium are derived. We explored spatial stability in the presence of diffusion and developed the criterion for diffusion-driven instability. Using amplitude equations, we then investigated the selection of Turing patterns around the Turing bifurcation threshold. The examination of the stability of these amplitude equations led to the discovery of numerous Turing patterns. Finally, numerical simulations were performed to validate the outcomes of the analysis. The outcomes of the theoretical study and numerical simulation were accorded. Our findings demonstrate that spatial patterns are sensitive to dispersal and predator death rates.

Periodic solution of a discrete commensal symbiosis model with Hassell-Varley type functional response

Abstract A non-autonomous discrete commensal symbiosis model with Hassell-Varley type functional response is proposed and studied in this paper. Sufficient conditions are obtained for the existence of positive periodic solution of the system.

Almost periodic dynamics of delayed prey–predator model with discontinuous harvesting policies and Hassell–Varley type functional response

In this study, a class of delayed prey–predator model with Hassell–Varley type functional response is investigated, in which the harvesting policies are modeled by discontinuous functions. Based on functional differential inclusions and set-valued analysis theories, the local and global existence of positive solution in sense of Filippov is given. By employing theory of functional differential inclusions and generalized differential inequalities, some sufficient conditions which guarantee the permanence of the system are obtained. According to non-smooth analysis theory with generalized Lyapunov functional approach, a series of useful criteria on existence, uniqueness and global asymptotic stability of the almost positive periodic solution to the system are derived. Some suitable examples together with their numerical simulations are given to illustrate the effectiveness of our results by using MATLAB.

Existence of Positive Periodic Solutions for a Neutral Delay Predator–Prey Model with Hassell–Varley Type Functional Response and Impulse

In this paper, we discuss a neutral delay predator–prey model with Hassel–Varley type functional response and impulse is investigated. By using Mawhin coincidence degree theory, we obtain some sufficient conditions for the existence of positive periodic solutions. We extend some known work.

Positive Almost Periodic Solutions for a Delayed Predator–Prey Model with Hassell-Varley Type Functional Response

By means of a fixed point theorem of coincidence degree theory, sufficient conditions are established for the existence of a positive almost periodic solution to a kind of delayed predator–prey model with Hassell-Varley type functional response. The method used in this paper offers a possible means to study the existence of positive almost periodic solutions to the models in biological populations. Finally, an example as well as numerical simulations are given to illustrate the feasibility and effectiveness of our results.

Dynamical Behavior for a Stochastic Predator–Prey Model with HV Type Functional Response

This paper establishes the existence-and-uniqueness theorem of a stochastic delayed predator–prey model with Hassell–Varley type functional response and examines stochastically ultimate boundedness, extinction and global asymptotic stability of this solution. It is interesting to note that the results are based on time-varying delay, which is different from the previous work (the results are delay-independent). Some numerical simulations are introduced to support the analytical findings.

Periodic solutions for a neutral delay Hassell–Varley type predator–prey system

The main aim of this paper is to discuss the neutral predator–prey model with Hassell–Varley type functional response and two time-varying delays. Some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem. Finally, numerical simulations are then carried out as supporting evidences of our analytical results.

Dynamics of a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects

This paper is concerned with a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects. By using the fixed point theory based on monotone operator, some simple conditions are obtained for the existence of at least one positive periodic solution of the model. The existence result of this paper implies that the functional response on prey does not influence the existence of positive periodic solution of the model, which completes some results given in recent years. Further, by applying the comparison theorem in impulsive differential equations and constructing a suitable Lyapunov functional, the permanence and global attractivity of the model are also investigated. The main results in this paper extend, complement, and improve the previously known result. And some examples and numerical simulations are given to illustrate the feasibility and effectiveness of the main results. Copyright © 2015 John Wiley & Sons, Ltd.

Oscillations for a delayed predator–prey model with Hassell–Varley-type functional response

In this paper, a delayed predator–prey model with Hassell–Varley-type functional response is investigated. By choosing the delay as a bifurcation parameter and analyzing the locations on the complex plane of the roots of the associated characteristic equation, the existence of a bifurcation parameter point is determined. It is found that a Hopf bifurcation occurs when the parameter τ passes through a series of critical values. The direction and the stability of Hopf bifurcation periodic solutions are determined by using the normal form theory and the center manifold theorem due to Faria and Maglhalaes (1995). In addition, using a global Hopf bifurcation result of Wu (1998) for functional differential equations, we show the global existence of periodic solutions. Some numerical simulations are presented to substantiate the analytical results. Finally, some biological explanations and the main conclusions are included.

Asymptotic behavior of a non-autonomous predator-prey model with Hassell–Varley type functional response and random perturbation

This paper considers a new non-autonomous predator-prey model with stochastic perturbation and Hassell–Varley type functional response. Based on classical comparison theorem of stochastic equations, $$It\hat{o}$$ ’s formula and skillful analysis techniques, the existence of a global positive solution and stochastically ultimate boundedness are derived. Furthermore, some sufficient and necessary criteria for extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and the global attractivity of the system are obtained. At last, a series of numerical simulations to illustrate our mathematical findings are presented and some conclusions are also given.

On a non-selective harvesting prey–predator model with Hassell–Varley type functional response

In this paper, a nonautonomous delayed prey–predator model with non-selective harvesting and Hassell–Varley type functional response is investigated. Some sufficient conditions are obtained for the existence of positive periodic solutions to the system using the continuation theorem of coincidence degree theory. Moreover, the obtained results are different from the previous works. Numerous are conducted to illustrate the feasibility of the obtained results.

On the Dynamics of a Nonautonomous Predator-Prey Model with Hassell-Varley Type Functional Response

The dynamic behaviors of a nonautonomous system for migratory birds with Hassell-Varley type functional response and the saturation incidence rate are studied. Under quite weak assumptions, some sufficient conditions are obtained for the permanence and extinction of the disease. Moreover, the global attractivity of the model is discussed by constructing a Lyapunov function. Numerical simulations which support our theoretical analysis are also given.

Positive periodic solutions for a nonautonomous neutral delay prey-predator model with impulse and Hassell-Varley type functional response

Positive periodic solutions for a nonautonomous neutral delay prey-predator model with impulse and Hassell-Varley type functional response

Positive periodic solutions in a non-selective harvesting predator–prey model with multiple delays

This paper is concerned with a predator–prey model with Hassell–Varley type functional response, non-selective harvesting and multiple delays. Some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem. In addition, the results are delay-dependent, which is different from the previous work. Finally, simulations illustrate the effectiveness of our results.

Periodic solutions to a delayed predator–prey model with Hassell–Varley type functional response

In this paper, a delayed predator–prey model with Hassell–Varley type functional responses is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions to it by applying the coincidence degree theorem. It is interesting that the result is based on the delay, which is different from the previous work (the results are delay-independent). Furthermore, the simulation shows that some conditions are sharp.

Permanence and Global Attractivity of Discrete Predator-Prey System with Hassell-Varley Type Functional Response

By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the discrete predator-prey system with Hassell-Varley type functional response are obtained. Example together with its numerical simulation shows that the main results are verifiable.

Global dynamics of a Predator-Prey model with Hassell-Varley Type functional response

Predator-prey models with Hassell-Varley type functional response are appropriate for interactions where predators form groups and have applications in biological control. Here we present a systematic global qualitative analysis to a general predator-prey model with Hassell-Varley type functional response. We show that the predator free equilibrium is a global attractor only when the predator death rate is greater than its growth ability. The positive equilibrium exists if the above relation reverses. In cases of practical interest, we show that the local stability of the positive steady state implies its global stability with respect to positive solutions. For terrestrial predators that form a fixed number of tight groups, we show that the existence of an unstable positive equilibrium in the predator-prey model implies the existence of an unique nontrivial positive limit cycle.

Assessing top‐down and bottom‐up control in a litter‐based soil macroinvertebrate food chain

The relative importance of top‐down and bottom‐up control in setting the equilibrium abundances within trophic levels is examined in a comparative study on the litter‐based food chain of a temperate deciduous forest. During two consecutive years, we estimated the abundances of macroinvertebrate detritivores and their predators on a natural gradient of annual litterfall. Detritus‐based food chains are thought to be classical examples of donor‐controlled systems. Indeed, both trophic levels showed higher abundances on sites with higher annual litterfall. Therefore, they appear to be bottom‐up controlled. Using the Errors‐in‐Variables regression technique, we quantitatively compared our data with the equilibrium predictions of a set of simple trophic chain models including bottom‐up effects with different types of functional responses (Beddington‐DeAngelis, Hassell‐Varley, and ratio‐dependent). The model with a Hassell‐Varley type functional response yielded the best adjustment to the data, although with a very high value of the mutual interference parameter suggesting the existence of overcompensating density dependence. Several changes to the structure of this model were considered. Their adjustment to the data consistently yielded such high values of the interference parameter.