TY - JOUR
T1 - Impact of Predator Signals on the Stability of a Predator–Prey System
T2 - A Z-Control Approach
AU - Nadim, Sk Shahid
AU - Samanta, Sudip
AU - Pal, Nikhil
AU - ELmojtaba, Ibrahim M.
AU - Mukhopadhyay, Indranil
AU - Chattopadhyay, Joydev
N1 - Funding Information:
Authors are thankful to the learned reviewers for their useful comments and suggestions, which help us to improve the manuscript. Research work of Sk Shahid Nadim is supported by the Senior Research Fellowship from the CSIR, Government of India.
Publisher Copyright:
© 2018, Foundation for Scientific Research and Technological Innovation.
PY - 2022/4
Y1 - 2022/4
N2 - 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.
AB - 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.
KW - Bi-stability
KW - Ecosystem conservation
KW - Fear effect
KW - Predator signals
KW - Subcritical and supercritical Hopf bifurcation
KW - Z-control
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U2 - 10.1007/s12591-018-0430-x
DO - 10.1007/s12591-018-0430-x
M3 - Article
AN - SCOPUS:85081372335
SN - 0971-3514
VL - 30
SP - 451
EP - 467
JO - Differential Equations and Dynamical Systems
JF - Differential Equations and Dynamical Systems
IS - 2
ER -