Persistence and global stability of Bazykin predator–prey model with Beddington–DeAngelis response function

Sarwardi, Sahabuddin; Haque, Mainul; Mandal, Prashanta Kumar

doi:10.1016/j.cnsns.2013.05.029

Cited by 41 publications

(21 citation statements)

References 25 publications

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“…In [23], a theoretical analysis of prey-predator model which incorporates Beddington-DeAngelis functional response with and without diffusion is discussed. Persistence and global stability of a prey-predator model incorporating Beddington-DeAngelis functional response is explored in [24]. One can find the dynamical analysis of density-dependent prey-predator system with Beddington-DeAngelis functional response in [9].…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge

2014

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This paper discusses a prey-predator model with reserved area. The feeding rate of consumers (predators) per consumer (i.e., functional response) is considered to be Beddington-DeAngelis type. The Beddington-DeAngelis functional response is similar to the Holling type II functional response but contains an extra term describing mutual interference by predators. We investigate the role of reserved region and degree of mutual interference among predators in the dynamics of system. We obtain different conditions that affect the persistence of the system. We also discuss local and global asymptotic stability behavior of various equilibrium solutions to understand the dynamics of the model system. The global asymptotic stability of positive interior equilibrium solution is established using suitable Lyapunov functional. It is found that the Hopf bifurcation occurs when the parameter corresponding to reserved region (i.e., m) crosses some critical value. Our result indicates that the predator species exist so long as prey reserve value (m) does not cross a threshold value and after this value the predator species extinct. To mimic the real-world scenario, we also solve the inverse problem of estimation of model parameter (m) using the sampled data of the system. The results can also be interpreted in different contexts such as resource conservation, pest management and

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Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge

2014

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“…Sarwardi, Haque and Mandal [38] have given similar condition for the stability of axial equilibrium point E 1 of the Beddington-type predator-prey model. Since…”

Section: 42mentioning

confidence: 77%

“…A model incorporating density dependent predator death rate was considered in [56]. Some other theories on the predator-prey model in which predator has density dependence can be found in [4,5,6,38,40]. Kratina et al [5] has clearly demonstrated and established the fact that the predator dependence is important not only at very high predator densities in the predator's functional response but also at low predator densities.…”

Section: Accepted Manuscriptmentioning

confidence: 97%

“…Bazykin and his colleagues [4] have studied a predatorprey model (Bazykin predator-prey model) with prey dependent functional response with predator having density dependence. During the past few years, Bazykin predator-prey model was modified and studied by considering a ratio-dependent functional response and Beddington-DeAngelis functional response (see [6,38,40]). A predator-prey system in which the predator has density dependence, incorporating Beddington-DeAngelis functional response has been proposed and studied in [6].…”

Section: Accepted Manuscriptmentioning

confidence: 99%

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Global analysis of a delayed density dependent predator–prey model with Crowley–Martin functional response

Tripathi

Tyagi

Abbas

2016

Communications in Nonlinear Science and Numerical Simulation

112

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“…Song and Yuan [15] and Sun et al [16] studied the bifurcation of a population dynamic model with delay and established the global stability and direction of global Hopf bifurcation simultaneously. Sarwardi et al [17] studied the properties of Hopf bifurcation in a modified Bazykin predator prey model with Beddington-DeAngelis type functional response and descrete delay. The parametric space under which the system enters into Hopf bifurcation for both delay and non-delay cases are also investigated.…”

Section: Introductionmentioning

confidence: 99%

Modeling the effect of mutual interference in a delay-induced predator-prey system

Upadhyay

Agrawal

2014

J. Appl. Math. Comput.

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In this paper, we investigate the effect of mutual interference on the dynamics of a predator-prey system with gestation delay. It has been observed that there is stability switches and system becomes unstable due to the combine effect of mutual interference and time delay. We determine the conditions under which the model system becomes globally asymptotically stable around the non-zero equilibria. By applying the normal form theory and the center manifold theorem, the explicit formulae which determine the stability and direction of the bifurcating periodic solutions are determined. Computer simulations have been carried out to illustrate different analytical findings.

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Persistence and global stability of Bazykin predator–prey model with Beddington–DeAngelis response function

Cited by 41 publications

References 25 publications

Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge

Dynamical analysis of a prey–predator model with Beddington–DeAngelis type function response incorporating a prey refuge

Global analysis of a delayed density dependent predator–prey model with Crowley–Martin functional response

Modeling the effect of mutual interference in a delay-induced predator-prey system

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