Influence of dispersal and strong Allee effect on a two-patch predator–prey model

Saha, Sangeeta; Samanta, G. P.

doi:10.1007/s40435-018-0490-3

Cited by 24 publications

(13 citation statements)

References 57 publications

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“…Such models are widely spread and intensively studied in related literature. Particularly, models with Allee-threshold extinction control mechanism present the advantage of capturing such variations of species growth rate by setting a maximum value to reach for population size to not go extinct [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of a Predator-Prey Model with Allee Threshold Applied to Online Social Network Users’ Data Forwarding

Zhang

Koura

2020

Mathematical Problems in Engineering

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We consider a predator-prey relationship in a fair system in which interacting species have different needs of resources to survive. We analyzed qualitatively the outcome of interaction using a modified logistic predator-prey model with Allee threshold in both predator and prey equations. We showed that the system had very rich dynamical behavior as stability around fixed points and periodic solutions could be obtained at certain conditions. Interaction outcome is highly submitted to initial conditions, species behavior, and the threshold applied. Numerical results suggested adapting resource allocation and the threshold value to optimize ecosystem sustainability.

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Section: Introductionmentioning

confidence: 99%

Asymptotic Behavior of a Predator-Prey Model with Allee Threshold Applied to Online Social Network Users’ Data Forwarding

Zhang

Koura

2020

Mathematical Problems in Engineering

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“…During the last years, many scholars did works on the continuous time Logistic model and related system with feedback controls (see, e.g., [16][17][18][19][20][21][22] and references cited therein). In 1992, Gopalsamy introduced a certain differential equation as a feedback control variable into the logistic models and discussed the asymptotic behavior of solutions for the model with feedback controls [16].…”

Section: Introductionmentioning

confidence: 99%

“…e global asymptotical stability of a logistic equation with feedback control was considered by means of a method combined with the upper and lower solution technique in [17]. In [18], influence of dispersal and strong Allee effect on a two-patch predator-prey model was studied and existence and stability criterion of the interior equilibrium point of the system was analyzed in presence as well as in absence of dispersal speed. Feedback control strategy was introduced into an SI epidemic model, the effect of population migration among n(n ≥ 2) different patches was considered, and globally asymptotically stable conditions for the unique endemic equilibrium was given by means of the method of global Lyapunov functions and results from graph theory [22].…”

Section: Introductionmentioning

confidence: 99%

Global Stability for a Semidiscrete Logistic System with Feedback Control

Lou

Han

2020

Discrete Dynamics in Nature and Society

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In this paper, a semidiscrete logistic model with the Dirichlet boundary conditions and feedback controls is proposed. By means of the sub- and supper-solution method and eigenvalue theory, the unique positive equilibrium is proved. By constructing a suitable Lyapunov function, the global asymptomatic stability of the unique positive equilibrium is investigated. Finally, numerical simulations are presented to verify the effectiveness of the main results.

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“…Rahmat [9] analyzes that inbreeding in a population can cause problems in the survival of the population, such as the reduction of birth weight and fertility, that will reduce the survival of the population itself. Nowadays, there are still lots of research on the Alee effect in a predator prey type of system, see [10,2,11,8]. This factor adds up an interesting dynamics to the model.…”

Section: Introductionmentioning

confidence: 99%

On Competition between Javan Rhino (Rhinoceros Sondaicus) and Javan Bull (Bos Javanicus) at Ujung Kulon National Park with Allee Effect

Harjanto

Mentari

2019

Communication in Biomathematical Sciences

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In the last few decades, it has been reported that the population of Rhino (Rhinoceros Sondaicus) at the Ujung Kulon National Park has been reaching a stagnation at the number 50s, despite the existing territory can support a much larger number of Rhinos. Here, we construct a dynamical model representing the interaction between Rhino and Bull (Bos Javanicus) with Allee effect for the Javan rhinos population. This Allee effect may occur in the field, among others, due to the solitary behaviour of Rhino within large territory, imbalance of age structure and gender and difficulty of finding mates in Javan rhinos population which causes inbreeding in the population. In this paper, we follow the previous paper on the territorial competition between Javan rhino and Javan bull at Ujung Kulon National Park and add Allee effect factor on the Javan rhino's population. We give a proof on the boundedness of the solution and explanation on the bifurcations that occur in the model. One of these bifurcations plays an important role in the system. Some simulations and suggestion on how to improve the survival of Javan rhino is also included.

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Influence of dispersal and strong Allee effect on a two-patch predator–prey model

Cited by 24 publications

References 57 publications

Asymptotic Behavior of a Predator-Prey Model with Allee Threshold Applied to Online Social Network Users’ Data Forwarding

Asymptotic Behavior of a Predator-Prey Model with Allee Threshold Applied to Online Social Network Users’ Data Forwarding

Global Stability for a Semidiscrete Logistic System with Feedback Control

On Competition between Javan Rhino (Rhinoceros Sondaicus) and Javan Bull (Bos Javanicus) at Ujung Kulon National Park with Allee Effect

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