Global stability and persistence in LG–Holling type II diseased predator ecosystems

The objective of this paper is to study the dynamical behaviour systematically of an ecological system with Beddington-DeAngelis functional response which avoids the criticism occurred in the case of ratio-dependent functional response at the low population density of both the species. The essential mathematical features of the present model have been analyzed thoroughly in terms of the local and the global stability and the bifurcations arising in some selected situations as well. The threshold values for some parameters indicating the feasibility and the stability conditions of some equilibria are also determined. We show that the dynamics outcome of the interaction among the species are much sensitive to the system parameters and initial population volume. The ranges of the significant parameters under which the system admits a Hopf bifurcation are investigated. The explicit formulae for determining the stability, direction and other properties of bifurcating periodic solutions are also derived with the use of both the normal form and the central manifold theory (cf. Carr [1]). Numerical illustrations are performed finally in order to validate the applicability of the model under consideration.Mathematics Subject Classification: 92D25, 92D30, 92D40.

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“…The time derivative of L along with the solutions of the system (2.1) gives (cf. Sarwardi et al [25], [29])…”

Section: )mentioning

confidence: 98%

Dynamical behaviour of an ecological system with Beddington–DeAngelis functional response

Sarwardi

Mandal

Gazi

2016

Model. Earth Syst. Environ.

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“…Persistence and equilibria global stability appear in [115] for this ecosystem extension with intraspecific competition due to infected predators and of a satiation effect modeled by HTII nonlinearities.…”

Section: Ecoepidemics With Leslie-gower Dynamicsmentioning

confidence: 96%

Ecoepidemiology: a More Comprehensive View of Population Interactions

Venturino

2015

Math. Model. Nat. Phenom.

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Abstract. Models proposed for the description of population interactions with pathogenic agents are presented. We review some basic quadratic-interactions models, then move to more complex demographics, structured models, models involving several populations, delays, plankton dynamics, the Allee effect and group behavior. In most of these cases basic reproduction numbers are evaluated and commented.

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“…Similarly, some scholars proposed and investigated the ecoepidemic models with disease in predators. Sarwardi et al [20] and Shaikh et al [21] studied a Leslie-Gower Holling type II predator-prey model with disease in predator and Leslie-Gower Holling type III predator-prey model with disease in predator, respectively. Some other ecoepidemic models with disease in predators one can refer to include [22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate

Xia

Kundu

Maitra

2018

Journal of Function Spaces

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A delayed ecoepidemic model with ratio-dependent transmission rate has been proposed in this paper. Effects of the time delay due to the gestation of the predator are the main focus of our work. Sufficient conditions for local stability and existence of a Hopf bifurcation of the model are derived by regarding the time delay as the bifurcation parameter. Furthermore, properties of the Hopf bifurcation are investigated by using the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out in order to validate our obtained theoretical results.

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Global stability and persistence in LG–Holling type II diseased predator ecosystems

Cited by 36 publications

References 18 publications

Dynamical behaviour of an ecological system with Beddington–DeAngelis functional response

Dynamical behaviour of an ecological system with Beddington–DeAngelis functional response

Ecoepidemiology: a More Comprehensive View of Population Interactions

Hopf Bifurcation of a Delayed Ecoepidemic Model with Ratio-Dependent Transmission Rate

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