We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey popu...We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey population has been classified into two categories, namely susceptible prey, infected prey where as the predator population remains free from infection. To investigate the behaviour of prey population we incorporate prey refuge in this model. Since the prey refuge decreases the predation rate then it has an important effect in our predator-prey interaction model. We have discussed the existence of various equilibrium points and local stability analysis at those equilibrium points. We investigate the Hopf-bifurcation analysis about the interior equilibrium point by taking the rate of infection parameter and the prey refuge parameter as bifurcation parameters. The numerical analysis is carried out to support the analytical results and to discuss some interesting results that our model exhibits.展开更多
The role of geomorphic habitat type, drift cell scale, and geographic scale in defining fish use of nearshore habitats is poorly known, particularly for Pacific salmon and their prey. In this study, key areas of nears...The role of geomorphic habitat type, drift cell scale, and geographic scale in defining fish use of nearshore habitats is poorly known, particularly for Pacific salmon and their prey. In this study, key areas of nearshore habitat in central and western Strait of Juan de Fuca were categorized by geomorphic habitat type and assessed for fish use within a degraded （Elwha） and intact comparative drift cells over a one year period. Juvenile Chinook and coho salmon were also sampled for genetic analysis to define regional dispersal patterns. Key findings are： （1） Ecological function of the area＇s nearshore is complex, with very strong seasonal variation in fish use both within and across GMHT （geomorphic habitat type）; （2） GMHT link to nearshore function for fish use differs depending on the fish species and time of year. Surf smelt and sand lance were the most abundant. And they were seasonally used embayed, spit, and bluff shorelines more than lower rivers. Juvenile Chinook, coho, and chum salmon occurred in much lower density than forage fish species, and used lower rivers more than other GMHTs; （3） When GMHTs were combined and analyzed at the drift cell scale, the degraded drift cell had different ecological patterns than the intact drift cell; （4） Cross regional juvenile fish use of nearshore is an important component of habitat use： juvenile Chinook and coho from as far away as the Columbia River Oregon and Klamath River California utilize central Strait of Juan de Fuca shorelines. Forage fish species may do so as well. Drift cell and cross regional scales are therefore most important for accurately defining nearshore ecological function, management, and restoration actions.展开更多
The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By m...The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.展开更多
This work deals with a prey-predator model in an environment where the carrying capacities are assumed to be variable with time and one species feeds upon the other. Independent harvesting efforts are applied in eithe...This work deals with a prey-predator model in an environment where the carrying capacities are assumed to be variable with time and one species feeds upon the other. Independent harvesting efforts are applied in either species and asymmetrical intraguild predation occurs. A common resource is consumed by two competing species and at the same time predator also consumes the prey. At first we discuss the model under constant carrying capacity and make the conclusion that no limit cycle exists in this case. Then we discuss the model without intraspecific competition. Our main concern is to cover the above mentioned two cases together, i.e. the model with variable carrying capacity and intraspecific competition. We determine the steady states and examine the dynamical behavior. We also analyze the local and global stability of the interior equilibrium by Routh-Hurwitz criterion and a suitable Lyapunov function respectively. A Hopf bifur- cation occurs with respect to a parameter which is the ratio of predator＇s and prey＇s intrinsic growth rate. The possibility of bionomic equilibrium has been considered. The optimal harvest policy is formulated and solved with Pontryagin＇s maximum principle. Some numerical simulations are given to explain most of the analytical results.展开更多
In this paper, we consider a diffusive Holling-Tanner predator prey model with Smith growth subject to Neumann boundary condition. We analyze the local stability, exis- tence of a Hopf bifurcation at the co-existence ...In this paper, we consider a diffusive Holling-Tanner predator prey model with Smith growth subject to Neumann boundary condition. We analyze the local stability, exis- tence of a Hopf bifurcation at the co-existence of the equilibrium and stability of bifur- cating periodic solutions of the system in the absence of diffusion. Furthermore the Turing instability and Hopf bifurcation analysis of the system with diffusion are studied. Finally numerical simulations are given to demonstrate the effectiveness of the theoretical analysis.展开更多
In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial...In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.展开更多
This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model ar...This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.展开更多
The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the ...The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.展开更多
This paper presents a prey-predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilib...This paper presents a prey-predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey predator system parameter.展开更多
文摘We formulate and analyze a predator-prey model followed by Leslie-Gower model in which the prey population is infected by disease. We assume that the disease can only spread over prey population. As a result prey population has been classified into two categories, namely susceptible prey, infected prey where as the predator population remains free from infection. To investigate the behaviour of prey population we incorporate prey refuge in this model. Since the prey refuge decreases the predation rate then it has an important effect in our predator-prey interaction model. We have discussed the existence of various equilibrium points and local stability analysis at those equilibrium points. We investigate the Hopf-bifurcation analysis about the interior equilibrium point by taking the rate of infection parameter and the prey refuge parameter as bifurcation parameters. The numerical analysis is carried out to support the analytical results and to discuss some interesting results that our model exhibits.
文摘The role of geomorphic habitat type, drift cell scale, and geographic scale in defining fish use of nearshore habitats is poorly known, particularly for Pacific salmon and their prey. In this study, key areas of nearshore habitat in central and western Strait of Juan de Fuca were categorized by geomorphic habitat type and assessed for fish use within a degraded （Elwha） and intact comparative drift cells over a one year period. Juvenile Chinook and coho salmon were also sampled for genetic analysis to define regional dispersal patterns. Key findings are： （1） Ecological function of the area＇s nearshore is complex, with very strong seasonal variation in fish use both within and across GMHT （geomorphic habitat type）; （2） GMHT link to nearshore function for fish use differs depending on the fish species and time of year. Surf smelt and sand lance were the most abundant. And they were seasonally used embayed, spit, and bluff shorelines more than lower rivers. Juvenile Chinook, coho, and chum salmon occurred in much lower density than forage fish species, and used lower rivers more than other GMHTs; （3） When GMHTs were combined and analyzed at the drift cell scale, the degraded drift cell had different ecological patterns than the intact drift cell; （4） Cross regional juvenile fish use of nearshore is an important component of habitat use： juvenile Chinook and coho from as far away as the Columbia River Oregon and Klamath River California utilize central Strait of Juan de Fuca shorelines. Forage fish species may do so as well. Drift cell and cross regional scales are therefore most important for accurately defining nearshore ecological function, management, and restoration actions.
基金The research is supported by the Scientific Research Foundation of the Doctor Department of Hubei University of Technology.
文摘The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.
文摘This work deals with a prey-predator model in an environment where the carrying capacities are assumed to be variable with time and one species feeds upon the other. Independent harvesting efforts are applied in either species and asymmetrical intraguild predation occurs. A common resource is consumed by two competing species and at the same time predator also consumes the prey. At first we discuss the model under constant carrying capacity and make the conclusion that no limit cycle exists in this case. Then we discuss the model without intraspecific competition. Our main concern is to cover the above mentioned two cases together, i.e. the model with variable carrying capacity and intraspecific competition. We determine the steady states and examine the dynamical behavior. We also analyze the local and global stability of the interior equilibrium by Routh-Hurwitz criterion and a suitable Lyapunov function respectively. A Hopf bifur- cation occurs with respect to a parameter which is the ratio of predator＇s and prey＇s intrinsic growth rate. The possibility of bionomic equilibrium has been considered. The optimal harvest policy is formulated and solved with Pontryagin＇s maximum principle. Some numerical simulations are given to explain most of the analytical results.
文摘In this paper, we consider a diffusive Holling-Tanner predator prey model with Smith growth subject to Neumann boundary condition. We analyze the local stability, exis- tence of a Hopf bifurcation at the co-existence of the equilibrium and stability of bifur- cating periodic solutions of the system in the absence of diffusion. Furthermore the Turing instability and Hopf bifurcation analysis of the system with diffusion are studied. Finally numerical simulations are given to demonstrate the effectiveness of the theoretical analysis.
基金Acknowledgments The authors thank the editor and referees for their valuable comments and suggestions. This work is supported by the National Basic Research Program of China （2010CB732501） and the National Natural Science Foundation of China （61273015）, the NSFC Tianyuan Foundation （Grant No. 11226256） and the Zhejiang Provincial Natural Science Foundation of China （Grant No. LY13A010010）, Zhejiang Provincial Natural Science Foundation of China LQ13A010023）.
文摘In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis functional response and Allee effect, and show that there is a unique global positive solution to the system with the positive initial value. Sufficient conditions for global asymptotic stability are established. Some simulation figures are introduced to support the analytical findings.
文摘This paper focuses on the stabilities of the equilibria to a predator-prey model with stage structure incorporating prey refuge. By analyzing the characteristic functions, we obtain that the equilibria of the model are locally stable when some suitable conditions are being satisfied. According to the comparison theorem and iteration technique, the globally asymptotic stability of the positive equilibrium is discussed. And, the sufficient conditions of the global stability to the trivial equilibrium and the boundary equilibrium are derived. The study shows that the prey refuge will enhance the density of the prey species, and it will decrease the density of predator species. Finally, some numerical simulations are carried out to show the efficiency of our main results.
文摘The goal of this paper is to investigate the dynamics of a non-autonomous density- dependent predator-prey system with Beddington-DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator-prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. ~rther, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed- point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.
文摘This paper presents a prey-predator model considering the predator interacting with non-refuges prey by class of functional responses. Here we also consider harvesting for only non-refuges prey. We discuss the equilibria of the model, and their stability for hiding prey either in constant form or proportional to the densities of prey population. We also investigate various possibilities of bionomic equilibrium and optimal harvesting policy. Finally we present numerical examples with pictorial presentation of the various effects of the prey predator system parameter.
