Debasis Mukherjee

Uniform persistence in a generalized prey-predator system with parasitic infection.

This paper deals with a generalized prey-predator system where the prey population is infected by a microparasite. The model is described by a system of three autonomous ordinary differential equations. Conditions for persistence of all populations are given. Impermanence criteria are also derived.

Permanent coexistence in a resource-based competition system

Abstract This paper deals with the permanent coexistence and global stability of a simple Lotka-Volterra type mathematical model of a living resource supporting two competing predators. The result include the sufficient condition for uniform persistence (or permanence) of the system. It is also shown that the system is globally asymptotically stable.

Global stability of prey-predator systems with predatory switching

This paper deals with a complex prey-predator system, consisting of two prey species and two types of predator (dominant and mutant of the same species) with predatory switching. We derived conditions for existing polymorphism with respect to a switching property and found a condition for feasible equilibrium to be globally asymptotically stable. We have shown parameter regions for a stable and an unstable feasible equilibrium.

Uniform persistence and global stability of two prey-predator pairs linked by competition.

General models of two predator-prey systems are considered in which the prey are linked through competition and the predators are not directly linked. The persistence criteria based upon a technique developed by Gard is obtained. In addition, a condition for the global asymptotic stability of the interior equilibrium is discussed.

On local(ly) ESS of a pair of prey–predator system with predatory switching

This paper concentrates on the study of ecological stability for guaranteeing evolutionary stable strategies (ESS) in a two pre-predator system taking into consideration of handling time, with predatory switching. Here predators are polyphagous in nature. The conditions for ESS of the model system are obtained at the equivalence point. We also derive the invasion conditions of a mutant predator.

Ratio dependent predation :A bifurcation analysis

In this study, we have considered a prey-predator model reflecting the predator interference with discrete time delay. This delay is regarded as the lag due to gestation. In absence of delay, the criteria for existence of interior equilibrium and its global stability are derived. By choosing the delay as a bifurcation parameter, we have shown that a Hopf bifurcation may occur when the delay passes its critical value. Finally, we have derived the criteria for stability switches and verified the results through computer simulation.

The effect of diffusion on two predators exploiting a resource

This paper deals with the stabilizing effect of diffusion on a system of a living resource supporting two noncompeting predators. It is shown that while the three species mathematical model without diffusion is unstable, the model with diffusion is asymptotically stable provided the diffusion coefficient of the resource exceeds a certain threshold value.

Formation of a regular dissipative structure: a bifurcation and non-linear analysis

A non-linear reaction diffusion model of a negative feedback epigenetic control system is presented. The model involves synthesis of the mitotic inducing and inhibiting proteins, simultaneously with intercellular self-diffusion and cross-diffusion of the latter only. The importance of negative cross-diffusion for creating a regular dissipative structure is shown. A bifurcation analysis of the non-linear diffusive system has been performed and it is concluded that bifurcation is supercritical. Lastly, using Liapunovs direct method, it is shown that the pattern evolved by the system is globally asymptotically stable.

Effect of time lag on non-living resource in a simple food chain

This paper deals with a system of one non-living resource detritus, detritivores and their predators where time delay has been considered in the detritus formation. Local stability criteria are derived in the absence of delays. Conditions are derived under which there can be no change of stability whatever the value of time lag and finally we obtain criteria under which the system admits a finite number of stability switchings as the time lag increases.

Global stability results of epidemiological models with nonlinear incidence rates

In this paper, we have observed the global behaviour of an epidemiological SEIRS model with nonlinear incidence rates @lI^pS^q by constructing a suitable Liapunov function. Moreover, we have found the conditions for global existence of a SEIS model by using Bendixon-Dulac criterion.