Impact of Predator Signals on the Stability of a Predator–Prey System: A Z-Control Approach

Sk Shahid Nadim, Sudip Samanta, Nikhil Pal, Ibrahim M. ELmojtaba, Indranil Mukhopadhyay, Joydev Chattopadhyay*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In contrast to long standing view on predator–prey interactions that predators have only direct effect on prey by killing, recent field experimentation on terrestrial vertebrates showed that indirect effect of predators’ fear may alter the behavioral changes on prey, including foraging and reproduction. Usually, prey perceive the signals from predators (chemical and/or vocal cues) and change their life-history and behavior to reduce the probability of being killed. Recently, Wang et al. (J Math Biol 73:1179–1204, 2016) proposed and analyzed a predator–prey model by considering the fear effect on prey population. They concluded that the model dynamics may exhibit both supercritical and subcritical Hopf bifurcation, while the classical predator–prey model exhibits only supercritical Hopf bifurcation. The cost of fear on prey may dramatically reduce foraging and reproduction, which may change the ecosystem stability. In the present investigation, we explore the possible applications of fear in prey due to predators’ signals and error based Z-control mechanism by manipulating the abundance of predator population. Our results suggest that by manipulating or controlling the abundance of predator one can achieve a desired prey population density. We also observe that Z-control mechanism has the property to produce a stable steady-state or a stable limit cycle by excluding the bi-stability situation as observed by Wang et al. We perform extensive numerical simulations to illustrate our analytical findings.

Original languageEnglish
Pages (from-to)451-467
Number of pages17
JournalDifferential Equations and Dynamical Systems
Volume30
Issue number2
DOIs
Publication statusPublished - Apr 2022

Keywords

  • Bi-stability
  • Ecosystem conservation
  • Fear effect
  • Predator signals
  • Subcritical and supercritical Hopf bifurcation
  • Z-control

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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