Abstract
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.
Highlights
Many organisms go through multiple life stages as they proceed from birth to death
The research reported in this paper will help in studying the catastrophic regime shifts in coralreefs under the proliferation of predatory Pterois Volitans and the subsequent loss in herbivory
The model used in this paper is a direct extension of the stage-structured model studied in (Bhattacharyya & Pal, 2013) with adult Pterois Volitans as IG-predator, juvenile Pterois Volitans as IG-prey, and Parrotfish as their common resource under the assumption that juveniles can predate, but do not reproduce
Summary
Many organisms go through multiple life stages as they proceed from birth to death. A stage-structured model of population growth consists of juvenile and adult organisms where the juveniles have no reproductive ability (Wang & Chen, 1997). The role of time delay on ecosystem models has been investigated by Jiao, Yang, Cai and Chen (2009), and Dhar and Jatav (2013) 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 Figure 1. The model used in this paper is a direct extension of the stage-structured model studied in (Bhattacharyya & Pal, 2013) with adult Pterois Volitans as IG-predator, juvenile Pterois Volitans as IG-prey, and Parrotfish as their common resource under the assumption that juveniles can predate, but do not reproduce. + h)yA(s + τ2), and φ3(s) > l(s + τ1)
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