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

Abstract

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.

Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

“…In this paper, by introducing ratio-dependent functional response for the growth of Parrotfish and Pterois volitans and by considering refuge protection for Parrotfish, we obtain results that justify the real-field observations. The effect of cannibalism is not clearly stated in [20,21], whereas, in [22] it is observed that higher rate of cannibalism induces oscillation around the positive equilibrium. Since [22] is studied by means of a single-species stage-structured model, it could not be evaluated from this paper whether cannibalism of Pterois volitans actually reduces predation pressure on Parrotfish.…”

“…In this section we investigate the numerical approach as demonstrated in [20], the effect of various parameters on the qualitative behavior of the system using a default set of parameter values as given in Table 1. We first covert the original parameter values by using the transformations given in "Adimensionalization …”

“…Also, Hsu et al [19] observed that ratio-dependent predator-prey models exhibit complicated dynamics near the boundaries. Our mathematical model is a direct extension of the models studied in [20,21] under the assumption that algae is growing logistically and Parrotfish is growing on algae with a functional response which depends on the density of algae as well as Parrotfish. In our previous studies [22], it is observed that the system becomes oscillatory around the interior equilibrium when the invasion rate of Pterois volitans exceeds some certain critical threshold.…”

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

“…Motivated by their works, we have studied a stage-structured system (Bhattacharyya & Pal, 2013) with Parrotfish at the first trophic level, and juvenile and adult Downloaded by [New York University] at 16:28 01 July 2015…”

An ecological perspective on marine reserves in prey–predator dynamics

“…Mathematical biology has been applied in recent years to various problems in ecology [1,2]. Biologists and policy-makers often advocate marine protected areas (MPAs) on the basis that they provide economic benefits, though there is little evidence that such benefits actually occur [3][4][5][6].…”