Joydeb Bhattacharyya

Stage-structured cannibalism with delay in maturation and harvesting of an adult predator

A three-dimensional stage-structured predator–prey model is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with non-constant harvesting. Time lag in maturation of the predator is introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a supercritical Hopf bifurcation when the maturation time lag crosses a certain critical value. Computer simulations have been carried out to illustrate various analytical results.

Dynamics of a stage-structured system with harvesting and discrete time delays

A two-dimensional single-species stage-structured model is proposed and analyzed to study the effect of intraguild predation with harvesting of the adult species. Time lags in reproduction and maturation of the organism are introduced in the system and conditions for local asymptotic stability of steady states are derived. The length of the delay preserving the stability is also estimated. It is found that there are stability switches for time delays, and Hopf bifurcations when time delays cross through some critical values. The stability and direction of the Hopf bifurcations are determined by applying the normal form method and the center manifold theory. Computer simulations have been carried out to illustrate various analytical results.

The role of space in stage-structured cannibalism with harvesting of an adult predator

The dynamics of a predator-prey reaction-diffusion system with Holling type III functional response, where the predator has two stages, a juvenile stage and an adult stage, is proposed and analyzed to study the effect of predation with non-constant harvesting of an adult predator. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of predation. Local stability of the system is obtained in the absence of one or more organisms and in the presence of all the organisms. Moreover, it is shown that the system undergoes Hopf bifurcation when the intrinsic growth rate of herbivorous prey crosses certain critical value. Computer simulations have been carried out to illustrate various analytical results.

Hysteresis in coral reefs under macroalgal toxicity and overfishing

Macroalgae and corals compete for the available space in coral reef ecosystems.While herbivorous reef fish play a beneficial role in decreasing the growth of macroalgae, macroalgal toxicity and overfishing of herbivores leads to proliferation of macroalgae. The abundance of macroalgae changes the community structure towards a macroalgae-dominated reef ecosystem. We investigate coral-macroalgal phase shifts by means of a continuous time model in a food chain. Conditions for local asymptotic stability of steady states are derived. It is observed that in the presence of macroalgal toxicity and overfishing, the system exhibits hysteresis through saddle-node bifurcation and transcritical bifurcation. We examine the effects of time lags in the liberation of toxins by macroalgae and the recovery of algal turf in response to grazing of herbivores on macroalgae by performing equilibrium and stability analyses of delay-differential forms of the ODE model. Computer simulations have been carried out to illustrate the different analytical results.

Allelopathy of plasmid-bearing and plasmid-free organisms competing for two complementary resources in a chemostat

We consider a model of competition between plasmid-bearing and plasmid-free organisms for two complementary nutrients in a chemostat. We assume that the plasmid-bearing organism produces an allelopathic agent at the cost of its reproductive abilities which is lethal to plasmid-free organism. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of competition. Local stability of the system is obtained in the absence of one or both the organisms. Also, global stability of the system is obtained in the presence of both the organisms. Computer simulations have been carried out to illustrate various analytical results.

Dynamics of asymmetric intraguild predation with time lags in reproduction and maturation

A three dimensional (3D) stage-structured predator–prey model is proposed and analyzed to study the effect of intraguild predation with harvesting of the adult species. Time lags in reproduction and maturation of the organism are introduced in the system and conditions for local asymptotic stability of steady states of delay differential forms of the ODE model are derived. The length of the delay preserving the stability is also estimated. Moreover, it is shown that the system undergoes a Hopf bifurcation when the time lags cross certain critical values. The stability and direction of the Hopf bifurcations are determined by applying the normal form method and the center manifold theory. Computer simulations have been carried out to illustrate various analytical results.