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In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics. [ABSTRACT FROM AUTHOR]

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using Pontryagin maximum principle. The numerical simulations have been presented in support of the analytical findings. [ABSTRACT FROM AUTHOR]

This paper presents a prey-predator harvesting model with time delay for bifurcation analysis. We consider the parameters of the proposed model with imprecise data as form of interval in nature, due to the lack of precise numerical information of the biological parameters such as prey population growth rate and predator population decay rate. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey under impreciseness of the biological parameters. Parametric functional form of interval number with two parameters is introduced. This study reveals that not only delay and harvesting effort play a significant role on the stability on the system but also interval parameters play a crucial role on the stability of the system. Computer simulations of numerical examples are given to explain our proposed imprecise model. We also address critically the biological implications of our analytical findings with proper numerical example. [ABSTRACT FROM AUTHOR]

This paper presents three species harvesting model in which there is one predator species and two others are prey species. We derive boundedness and equilibrium point for this system. Also we derive the stability of this system analytically. We find bifurcation for this system. We have derived the binomic equilibrium point by using Pontryagin's maximum principle (PMP). Presented are various suitable analytical and numerical examples with Maple 18 programming. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a class of singular Leslie–Gower predator–prey bioeconomic models with environment fluctuations and time delays is investigated. Local stability analysis of the model reveals that there is a phenomenon of singularity induced bifurcation due to variation of economic interest of harvesting. By choosing the delay as a bifurcation parameter, it is shown that the Hopf bifurcations can occur as the delay crosses some critical values. Then, the effect of a fluctuating environment on the singular stochastic delayed predator–prey bioeconomic model is discussed. Finally numerical simulations demonstrate that the amplitude of oscillation for population is enhanced when compared with the oscillation observed in the deterministic environment. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a tritrophic predator–prey model with harvesting where the top-predator population is partially supported with alternative food. We report the consequences of providing alternative food to the top-predator in a top-predator harvested model. The extinction criterion for top-predator population, local stability of equilibrium points and persistence conditions are discussed theoretically. Pontryagins maximum principle is used to characterize the optimal control of harvesting. We have derived the condition of Hopf bifurcation by varying harvesting effort. The bifurcation diagrams of the system with respect to harvesting effort in presence of alternative food are given. Our analysis show that alternative food can prevent top-predator extinction risk at higher harvesting effort and plays a vital role for biological conservation of species. [Copyright &y& Elsevier]

Abstract: This paper describes a prey–predator model with stage structure for predator and selective harvesting effort on predator population. The Holling type II functional response function is taken into consideration. All the equilibria of the proposed system are determined and the behavior of the system is investigated near them. Local stability of the system is analyzed. Geometric approach is used to derive the sufficient conditions for global stability of the system. The occurrence of Hopf bifurcation of the model system in the neighborhood of the co-existing equilibrium point is shown through considering maximal relative increase of predation as bifurcation parameter. Fishing effort used to harvest predator population is considered as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. Pontryagin’s maximum principle is used to characterize the optimal control. The optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. [Copyright &y& Elsevier]

Abstract: This paper describes a prey–predator fishery model with stage structure for prey. The adult prey and predator populations are harvested in the proposed system. The dynamic behavior of the model system is discussed. It is observed that singularity induced bifurcation phenomenon is appeared when variation of the economic interest of harvesting is taken into account. We have incorporated state feedback controller to stabilize the model system in the case of positive economic interest. Fishing effort used to harvest the adult prey and predator populations is used as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. Pontryagin’s maximum principle is used to characterize the optimal control. The optimal system is derived and then solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. [Copyright &y& Elsevier]

Abstract: In this paper, we study an eco-epidemiological model where prey disease is modeled by a Susceptible-Infected (SI) scheme. Saturation incidence kinetics is used to model the contact process. The predator population adapt switching technique among susceptible and infected prey. The prey species is supposed to be commercially viable and undergo constant non-selective harvesting. We study the stability aspects of the basic and the switching models around the infection-free state and the infected steady state from a local as well as a global perspective. Our aim is to study the role of harvesting and switching on the dynamics of disease propagation and/or eradication. A comparison of the local and global dynamical behavior in terms of important system parameters is obtained. Numerical simulations are done to illustrate the analytical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, by employing the continuation theorem of coincidence degree theory, we establish an easily verifiable criteria for the existence of at least four positive periodic solutions for a discrete time delayed predator–prey system with nonmonotonic functional response and harvesting. [Copyright &y& Elsevier]

The purpose of this study is to explore an ecological Ammensal model with four species of Species- 1 i.e Ammensal Prey (PA), Species-2 i.e Ammensal Predator (QA), Species-3 i.e Ammensal Enemy (EA), and Species-4 i.e Enmity(N) with harvesting at variable rate(?). The System mainly consists of an Ammensal Prey (PA), a Ammensal Predator (QA) that survives on an Ammensal -prey(PA), Ammensal Enemy (EA) and Enmity(N) for which PA, QA are Ammensal, i.e., EA and N have an undesirable effect on PA and QA without being affected in any way. Furthermore, EA is enormous for N, and N is harmful to EA. First level Ammensalism is represented by the pair PA & EA, the pair of second level Ammensalism is QA & N and third level Ammensalism by the pair EA & N. The system's model equations form a set of four non-linear ordinary differential coupled equations of first order. There are sixteen equilibrium points found. The interactions between the four species are explored in light of different changes in various species' growth rate. [ABSTRACT FROM AUTHOR]

Provides information on a study concerning the development of a mathematical model for predation-prey metapopulation as a generalization of single-species metapopulation harvesting theory. Economic efficiency of predation and the protection of relative source prey; Observation concerning harvesting and seeding strategy.

First, a discrete stage-structured and harvested predator-prey model is established, which is based on a predator-prey model with Type III functional response. Then theoretical methods are used to investigate existence of equilibria and their local properties. Third, it is shown that the system undergoes flip bifurcation and Neimark-Sacker bifurcation in the interior of , by using the normal form of discrete systems, the center manifold theorem and the bifurcation theory, as varying the model parameters in some range. In particular, the direction and the stability of the flip bifurcation and the Neimark-Sacker bifurcation are showed. Finally, numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as cascades of period-doubling bifurcation and chaotic sets. These results reveal far richer dynamics of the discrete model compared with the continuous model. The Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. In addition, we show also the stabilizing effect of the harvesting by using numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, a prey-predator system with Holling type II functional response for the predator population including prey refuge region has been analyzed. Also a harvesting effort has been considered for the predator population. The density-dependent mortality rate for the prey, predator and super predator has been considered. The equilibria of the proposed system have been determined. Local and global stabilities for the system have been discussed. We have used the analytic approach to derive the global asymptotic stabilities of the system. The maximal predator per capita consumption rate has been considered as a bifurcation parameter to evaluate Hopf bifurcation in the neighborhood of interior equilibrium point. Also, we have used fishing effort to harvest predator population of the system as a control to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent is earned from the resource. Finally, we have presented some numerical simulations to verify the analytic results and the system has been analyzed through graphical illustrations. [ABSTRACT FROM AUTHOR]

We used a mathematical model to predict and explain the effect of harvesting combined with predation by the Nile perch on Nile tilapia. The model incorporates three developmental stages of each species. The findings show that uncontrolled human exploitation of the stock leads to loss of fish biodiversity in the lake. The results of the study also show that increasing harvesting rate of the mature Nile perch leads to stable stationary states of the system. However, increasing predation rates by Nile perch lead to unstable equilibria. Résumé Nous avons employé un modèle mathématique pour prédire et expliquer les effets, sur le tilapia du Nil, de la pêche à laquelle s'ajoute la prédation par la perche du Nil. Le modèle intègre trois stades de développement pour chaque espèce. Les résultats montrent que l'exploitation incontrôlée des stocks par les hommes entraîne une perte de la biodiversité des poissons dans le lac. Les résultats de l’étude montrent aussi que le taux croissant de pêche des perches du Nil mâtures conduit à des états stationnaires stables du système. Cependant, le taux croissant de la prédation par les perches du Nil entraîne un déséquilibre. [ABSTRACT FROM AUTHOR]

Harvesting of prey biomass is analyzed in an integrated ecological-economic system whose submodels, a predator–prey ecosystem and a simple economy, are microfounded dynamic general equilibrium models. These submodels are interdependent because the ecosystem responds to harvesting—through the reactions of optimizing individual organisms—by changing the provision of public ecosystem services to consumers. General analytical results are derived regarding the impact of harvesting policies on short-run equilibria of both submodels, on population dynamics, and on stationary states of the integrated model. A key insight is that prey biomass carries a positive ecosystem price which needs to be added as a tax mark-up to the economic price of harvested biomass to attain allocative efficiency. Further information on the dynamics is gained by resorting to numerical analysis of the policy regimes of zero harvesting, laissez-faire harvesting and efficient harvesting. [ABSTRACT FROM AUTHOR]