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Prahlad Majumdar

Bio: Prahlad Majumdar is an academic researcher from University of Calcutta. The author has contributed to research in topics: Bogdanov–Takens bifurcation & Hopf bifurcation. The author has an hindex of 2, co-authored 4 publications receiving 7 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors investigated the impact of predator harvesting in a two-dimensional prey-predator model with Holling type III functional response, and the main objective of this paper is to investigate the impact on predator survival.
Abstract: In the present paper we have investigated the impact of predator harvesting in a two-dimensional prey–predator model with Holling type III functional response. The main objective of this paper is t...

15 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigate the dynamical behavior of a two-species predator-prey model with Holling type IV functional response and nonlinear predator harvesting, and investigate the positivity and bo...
Abstract: The aim of this paper is to investigate the dynamical behavior of a two-species predator–prey model with Holling type IV functional response and nonlinear predator harvesting. The positivity and bo...

9 citations

Journal ArticleDOI
TL;DR: In this paper, an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate has been described, and the existence and stability analysis of equilibria have been investigated.
Abstract: This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point (DFE) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov-Takens bifurcation (BT) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.

9 citations

Posted ContentDOI
TL;DR: A tri-topic food web model with Beddington-DeAngelis functional response between interacting species is considered, incorporating the reduction of prey and intermediate predator growth because of the fear of intermediate and top predator respectively.
Abstract: The most important fact in the field of theoretical ecology and evolutionary biology is the strategy of predation for predators and avoidance of prey from predator attack. A lot of experimental works suggest that the reduction of prey depends on both direct predation and fear of predation. We explore the impact of fear effect and mutual interference among predators into a three-species food chain model. In this manuscript, we have considered a tri-topic food chain model with Beddington–DeAngelis functional response between interacting species, incorporating the reduction of prey and intermediate predator growth due to the fear of intermediate and top predator, respectively. We have provided parametric conditions for existence of biologically feasible equilibria as well as their local and global stability. We have established conditions of transcritical, saddle-node and Hopf bifurcation about different equilibria. Finally, we have performed some numerical investigations to justify analytical findings.

6 citations


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Book
01 Jan 1991
TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
Abstract: Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index

1,977 citations

Journal ArticleDOI
TL;DR: The proposed imprecise model is formulated by considering two more realistic factors: the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population.

17 citations

Journal ArticleDOI
TL;DR: In this paper , the authors studied the stability and local bifurcations of an imprecise prey-predator system in an uncertain environment, where they considered the effect of a fear factor on the growth rate of prey population and non-linear harvesting of predator population.

16 citations

Journal ArticleDOI
TL;DR: In this paper, a discrete-time predator-prey model with Holling type-III functional response and harvesting in both species was studied, and a detailed bifurcation analysis, depending on some parameter, was performed.
Abstract: In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, r...

11 citations