Predator Harvesting Research Articles

Balanced harvesting in two predators one prey system

In this research, we discuss balancing two essential ecosystem services, known as resilience and yield, in a harvested two predators one prey system. We study how these two ecosystem services respond to different types of harvesting plans applied to the system. In individual harvesting, we observe that prey harvesting is suitable for generating more yield while either predator harvesting gives more resilience. Several patterns are possible based on the intensity of harvesting efforts applied to prey or the predator in simultaneous harvesting. This study shows that a balanced harvest between prey and predators may give more than the selective harvesting of any species yielding and stabilizing the ecosystem. Even if this fair strategy is not a cooperative situation for both resilience and yield, it may be the most favorable approach to scale those services. Finally, we may state that it would help us correlate the safest position (corresponds to the maximizing resilience yield) and the good views (which corresponds to the maximum sustainable return) to safeguard our ecosystems.

The Complex Dynamical Behavior of a Prey-Predator Model with Holling Type-III Functional Response and Non-Linear Predator Harvesting

ABSTRACT In the present paper we have investigated the impact of predator harvesting in a two-dimensional prey–predator model with Holling type III functional response. The main objective of this paper is to study the change of dynamical behaviour of the prey–predator model in the presence of non-linear predator harvesting. The model system shows complex dynamics with the change of different system parameters. We have established the positivity and boundedness of the solutions under a certain parametric condition with non-negative initial conditions. The existence and stability criterion of different equilibrium points are investigated in terms of system parameters. We have shown that the system undergoes through saddle-node bifurcation, transcritical bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation under different parametric conditions. The structural changes or the system bifurcations predict the global dynamics of the model system. We have computed the first Lyapunov number to find the direction of the Hopf-bifurcating periodic solution of the system. Using numerical simulation we have studied here the effect of conversion efficiency, protection of the environment to the prey population and non-linear predator harvesting on the model dynamics. Finally the paper is ended with some conclusions.

Pattern formations of a delayed diffusive predator–prey model with predator harvesting and prey social behavior

In this research, we are interested in analyzing the behavior of a diffusive predator–prey model in the presence of predator rivalry and prey social behavior. The predator rivalry affects hugely the behavior of predator and the prey, so we are interested in analyzing the complex dynamics generated by the presence of predator harvesting and its influence on the behavior of the solution. For the mathematical purpose, we will concentrate on analyzing the system in the absence of diffusion where the existence of Hopf bifurcation is investigated; also, we proved that the presence of the time lags generates interesting patterns, which it can lead to instability even Hopf bifurcation. The stability of the homogeneous and nonhomogeneous periodic solution generated by the presence of Hopf bifurcation is established using the normal form. The mathematical obtained results are checked numerically using graphical representations.

Dynamics of a Stage-Structured-Prey and Predator Model with Linear Harvesting of Mature Prey and Predator

In this paper we have studied the dynamical behaviors of stage-structured-prey and predator model with linear harvesting of both mature prey and predator. Optimal harvesting policy, positivity, boundedness and Hopf-bifurcation have been studied. Finally, some graphical and numerical simulations are given in order to validate our analytical and theoretical findings.

Relationship between multiple ecosystem services and sustainability in three species food chain

The world fisheries are mainly focused on the yield from fishing, and hence maximum sustainable yield (MSY) policy has become the most popular management tool. But this aim of maximum productivity, particularly in the multitrophic system, impacts the resilience, considering the potential of the system to absorb the disturbances applied to the system. Due to harvesting effort used on different individual trophic levels, the trade-offs and synergies between yield and resilience of a tri-trophic food chain system have been studied. In Holling type II functional response, the enrichment of carrying capacity can destabilize the system and may adversely affect the system resilience. In the case of prey harvesting, for both Holling type I and II responses, the existence of MSY depends on some parametric restrictions, but resilience maximizing yield (RMY) always exists. For predator harvesting, only RMY may be a favorable harvesting strategy as MSY does not exist. But for the top predator harvesting with both for Holling type I and II functional responses, both the pair MSY and RMY exist. Either MSY, or RMY, or a balanced approach between them, maybe implemented depending upon the requirements of more yield, or more resilience, or balancing them.

Dynamical behaviors and optimal harvesting of an intraguild prey-predator fishery model with Michaelis-Menten type predator harvesting

The present paper discusses the dynamics and optimal harvesting of an intraguild prey-predator fishery model by incorporating the nonlinear Michaelis-Menten type of harvesting in predator. To our knowledge, there is limited literature working on Michaelis-Menten type of harvesting in a three species intraguild model with variable carrying capacity. The carrying capacity is proportional to the density of biotic resource. The existence of the possible equilibria has been studied along with the stability criteria. We consider the impact of predator fish harvesting as the bifurcation parameter to analyze the long time behavior of the proposed system. From the economic perspective, bionomic equilibrium of the system is studied and optimal harvesting policy is derived with the assistance of Pontryagin Maximum Principle. Finally, numerical results are presented to verify our analytical results. It is shown that in the bifurcation diagrams, the system can exhibit transcritical and Hopf bifurcations in the neighborhood of coexistence equilibrium at low and relatively high level of predator harvesting respectively. Interestingly, the system enters to a bistable region where both the coexistence and predator-free equilibria can be stable depending on the initial values. This bistable behavior might be novel to the existing literature that studied intraguild models with variable carrying capacity. The objective of this study is to derive the optimal threshold for the predator harvesting that gives maximum financial profit while sustaining the fishery resources.

Mathematical Analysis of an Eco-Epidemic Model with Different Functional Responses of Healthy and Infected Predators on Prey Species

This article describes a mathematical model for a predator-prey system with two types of functional responses and a transmissible disease in the predator species. The effect of stocking of healthy predator in healthy predator species class and harvesting of healthy predator are analyzed. The essential mathematical features of the proposed eco-epidemic system such as boundedness, positivity, local and global stability and Hopf bifurcation are discussed. Numerical simulations are also performed to validate the theoretical results obtained.

BIFURCATION ANALYSIS OF A TWO-DIMENSIONAL PREDATOR–PREY MODEL WITH HOLLING TYPE IV FUNCTIONAL RESPONSE AND NONLINEAR PREDATOR HARVESTING

The aim of this paper is to investigate the dynamical behavior of a two-species predator–prey model with Holling type IV functional response and nonlinear predator harvesting. The positivity and boundedness of the solutions of the model have been established. The considered system contains three kinds of equilibrium points. Those are the trivial equilibrium point, axial equilibrium point and the interior equilibrium points. The trivial equilibrium point is always saddle and stability of the axial equilibrium point depends on critical value of the conversion efficiency. The interior equilibrium point changes its stability through various parametric conditions. The considered system experiences different types of bifurcations such as Saddle-node bifurcation, Hopf bifurcation, Transcritical bifurcation and Bogdanov–Taken bifurcation. It is clear from the numerical analysis that the predator harvesting rate and the conversion efficiency play an important role in stability of the system.

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

The harvesting management is developed to protect the biological resources from over-exploitation such as harvesting and trapping. In this article, we consider a predator–prey interaction that follows the fractional-order Rosenzweig–MacArthur model where the predator is harvested obeying a threshold harvesting policy (THP). The THP is applied to maintain the existence of the population in the prey–predator mechanism. We first consider the Rosenzweig–MacArthur model using the Caputo fractional-order derivative (that is, the operator with the power-law kernel) and perform some dynamical analysis such as the existence and uniqueness, non-negativity, boundedness, local stability, global stability, and the existence of Hopf bifurcation. We then reconsider the same model involving the Atangana–Baleanu fractional derivative with the Mittag–Leffler kernel in the Caputo sense (ABC). The existence and uniqueness of the solution of the model with ABC operator are established. We also explore the dynamics of the model with both fractional derivative operators numerically and confirm the theoretical findings. In particular, it is shown that models with both Caputo operator and ABC operator undergo a Hopf bifurcation that can be controlled by the conversion rate of consumed prey into the predator birth rate or by the order of fractional derivative. However, the bifurcation point of the model with the Caputo operator is different from that of the model with the ABC operator.

Dynamical response of an eco-epidemiological system with harvesting

This article presents a study of Leslie–Gower predator–prey system to investigate the dynamics of disease transmission among predator species. The system includes the harvesting of infected predator. The positivity, boundedness of the solutions and permanence of the system are taken into consideration. The stability and Hopf bifurcation analyses around biologically feasible equilibria are scrutinized. The harvesting of infected predator plays a crucial role for the occurrence of limit cycle oscillations and stability around the interior equilibrium point. Our results disclose that infected predator harvesting has a considerable consequence on the eco-epidemiological system. The optimal control theory has been applied to investigate optimal strategies for controlling the infection. Analytical findings are confirmed through numerical simulations.

Chaos Detection and Optimal Control in a Cannibalistic Prey–Predator System with Harvesting

This paper deals with a stage-structured predator–prey system which incorporates cannibalism in the predator population and harvesting in both population. The predator population is categorized into two divisions; adult predator and juvenile predator. The adult predator and prey species are harvested via hypothesis of catch-per-unit-effort, whereas juveniles are safe from being harvested. Mathematically, the dynamic behavior of the system such as existing conditions of equilibria with their stability is studied. The global asymptotic stability of prey-free equilibrium point and nonzero equilibrium point, if they exist, is proved by considering respective Lyapunov functions. The system undergoes transcritical and Hopf–Andronov bifurcations. The impacts of predator harvesting rate and prey harvesting rate on the system are analyzed by taking them as bifurcation parameters. The route to chaos is discussed by showing maximum Lyapunov exponent to be positive with sensitivity dependence on the initial conditions. The chaotic behavior of the system is confirmed by positive maximum Lyapunov exponent and non-integer Kaplan–Yorke dimension. Numerical simulations are executed to probe our theoretic findings. Also, the optimal harvesting policy is studied by applying Pontryagin’s maximum principle. Harvesting effort being an emphatic control instrument is considered to protect prey–predator population, and preserve them also through an optimal level.

Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting

<p style='text-indent:20px;'>The objective of the current paper is to investigate the dynamics of a new bioeconomic predator prey system with only predator's harvesting and Holling type Ⅲ response function. The system is equipped with an algebraic equation because of the economic revenue. We offer a detailed mathematical analysis of the proposed model to illustrate some of the significant results. The boundedness and positivity of solutions for the model are examined. Coexistence equilibria of the bioeconomic system have been thoroughly investigated and the behaviours of the model around them are described by means of qualitative theory of dynamical systems (such as local stability and Hopf bifurcation). The obtained results provide a useful platform to understand the role of the economic revenue <inline-formula><tex-math id="M1">$ v $</tex-math></inline-formula>. We show that a positive equilibrium point is locally asymptotically stable when the profit <inline-formula><tex-math id="M2">$ v $</tex-math></inline-formula> is less than a certain critical value <inline-formula><tex-math id="M3">$ v^{*}_1 $</tex-math></inline-formula>, while a loss of stability by Hopf bifurcation can occur as the profit increases. It is evident from our study that the economic revenue has the capability of making the system stable (survival of all species). Finally, some numerical simulations have been carried out to substantiate the analytical findings.</p>

Spatiotemporal patterns in a diffusive predator-prey model with protection zone and predator harvesting

Abstract In this paper, a diffusive predator-prey model subject to the zero flux boundary conditions is considered, in which the prey population exhibits social behavior and the harvesting functional of the predator population is assumed to be considered in a quadratic form. The existence of a positive solution and its bounders is investigated. The global stability of the semi trivial constant equilibrium state is established. Concerning the non trivial equilibrium state, the local stability, Hopf bifurcation, diffusion driven instability, Turing-Hopf bifurcation are investigated. The direction and the stability of Hopf bifurcation relying on the system parameters is derived. Some numerical simulations are used to extend the analytical results and show the occurrence of the homogeneous and non homogeneous periodic solutions. Further the effect of the rivalry rate on the dynamical behavior of the studied species.

A Mathematical Study on a Diseased Prey-Predator Model with Predator Harvesting

In this paper, we present a mathematical model for a prey-predator system with infectious disease in the prey population. We assumed that there is harvesting from the predator and a defensive property against predation. This model is constituted by a system of nonlinear decoupled ordinary first order differential equations, which describe the interaction among the healthy prey, infected prey and predator. The existence, uniqueness and boundedness of the system solutions are investigated. Local stability of the system at equilibrium points is discussed.

Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator

The dynamics of predator-prey model with infectious disease in prey and harvesting in predator is studied. Prey is divided into two compartments i.e the susceptible prey and the infected prey. This model has five equilibrium points namely the all population extinction point, the infected prey and predator extinction point, the infected prey extinction point, and the co-existence point. We show that all population extinction point is a saddle point and therefore this condition will never be attained, while the other equilibrium points are conditionally stable. In the end, to support analytical results, the numerical simulations are given by using the fourth-order Runge-Kutta method.

Dynamics of Predator-Prey Community with Age Structures and Its Changing Due To Harvesting

The paper studies dynamic modes of discrete-time model of structured predator-prey community like “arctic fox – rodent” and changing its dynamic modes due to interspecific interaction. We paid special attention to the analysis of situations in which changes in the dynamic modes are possible. In particularly, 3-cycle emerging in prey population can result in predator extinction. Moreover, this solution corresponding to an incomplete community simultaneously coexists with the solution describing dynamics of complete community, which can be both stable and unstable. The anthropogenic impact on the community dynamics is studied, that is realized as harvest of some part of predator or prey population. It is shown that prey harvesting leads to expansion of parameter space domain with non-trivial stable numbers of community populations. In this case, the prey harvest has little effect on the predator dynamics; changes are mainly associated with multistability areas. In particular, the multistability domain narrows, in which changing initial conditions leads to different dynamic regimes, such as the transition to a stable state or periodic oscillations. As a result, community dynamics becomes more predictable. It is shown that the dynamics of prey population is sensitive to its harvesting. Even a small harvest rate results in disappearance of population size fluctuations: the stable state captures the entire phase space in multistability areas. In the case of the predator population harvest, stability domain of the nontrivial fixed point expands along the parameter of the predator birth rate. Accordingly, a case where predator determines the prey population dynamics is possible only at high values of predator reproductive potential. It is shown that in the case of predator harvest, a change in the community dynamic mode is possible because of a shifting dynamic regime in the prey population initiating the same nature fluctuations in the predator population. The dynamic regimes emerging in the community models with and without harvesting were compared.

Dynamics of Predator-Prey Community with Age Structures and Its Changing Due To Harvesting

The paper studies dynamic modes of discrete-time model of structured predator-prey community like “arctic fox – rodent” and changing its dynamic modes due to interspecific interaction. We paid special attention to the analysis of situations in which changes in the dynamic modes are possible. In particularly, 3-cycle emerging in prey population can result in predator extinction. Moreover, this solution corresponding to an incomplete community simultaneously coexists with the solution describing dynamics of complete community, which can be both stable and unstable. The anthropogenic impact on the community dynamics is studied, that is realized as harvest of some part of predator or prey population. It is shown that prey harvesting leads to expansion of parameter space domain with non-trivial stable numbers of community populations. In this case, the prey harvest has little effect on the predator dynamics; changes are mainly associated with multistability areas. In particular, the multistability domain narrows, in which changing initial conditions leads to different dynamic regimes, such as the transition to a stable state or periodic oscillations. As a result, community dynamics becomes more predictable. It is shown that the dynamics of prey population is sensitive to its harvesting. Even a small harvest rate results in disappearance of population size fluctuations: the stable state captures the entire phase space in multistability areas. In the case of the predator population harvest, stability domain of the nontrivial fixed point expands along the parameter of the predator birth rate. Accordingly, a case where predator determines the prey population dynamics is possible only at high values of predator reproductive potential. It is shown that in the case of predator harvest, a change in the community dynamic mode is possible because of a shifting dynamic regime in the prey population initiating the same nature fluctuations in the predator population. The dynamic regimes emerging in the community models with and without harvesting were compared.

A Prey-Predator Model with Michael Mentence Type of Predator Harvesting and Infectious Disease in Prey

A prey-predator model with Michael Mentence type of predator harvesting and infectious disease in prey is studied. The existence, uniqueness and boundedness of the solution of the model are investigated. The dynamical behavior of the system is studied locally as well as globally. The persistence conditions of the system are established. Local bifurcation near each of the equilibrium points is investigated. Finally, numerical simulations are given to show our obtained analytical results.

Degenerate Hopf bifurcation in a Leslie\u2013Gower predator\u2013prey model with predator harvest

In this paper, we investigate the degenerate Hopf bifurcation of a Leslie–Gower predator–prey system with predator harvest. The known work discussed the Hopf bifurcation of this system when the first Lyapunov number does not vanish and gave an example of a stable weak focus with order 2. However, the thorough discussion of center-type equilibrium for all possible parameters has not been completed. In this paper, by computing the first two focal values, we decompose the variety with resultant and prove that the center-type equilibrium is a weak focus with order at most 2 for all the possible parameter values. Moreover, numerical simulations are employed to show the appearance of two limit cycles from degenerate Hopf bifurcation. Our results finish the study of Hopf bifurcation in this system.

The Influence of Additive Allee Effect and Periodic Harvesting to the Dynamics of Leslie-Gower Predator-Prey Model

In this paper, the influence of additive Allee effect in prey and periodic harvesting in predator to the dynamics of the Leslie-Gower predator-prey model is proposed. We first simplify the model to the non-dimensional system by scaling the variable and transform the model into an autonomous system. If the effect Allee is weak, we have at most two equilibrium points, else if the Allee effect is strong, at most four equilibrium points may exist. Furthermore, the behavior of the system around equilibrium points is investigated. In the end, we give numerical simulations to support theoretical results.