Multiple stability switches and Hopf bifurcation in an age structured prey-predator system: effects of maturation and cooperative hunting delay

The classical prey-predator model assumes that prey species has no life history. But many species whose individuals have a life history with two classes, namely immature and mature. Since, immature prey can be easily captured by the predators because of their short life experiences and less activity...

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Bibliographic Details
Published in:Nonlinear dynamics 2024-10, Vol.112 (19), p.17585-17609
Main Authors: Sahu, S. R., Raw, S. N.
Format: Article
Language:English
Subjects:
Age
Automotive Engineering
Behavior
Birds
Birth rate
Classical Mechanics
Control
Cooperation
Delay
Dynamical Systems
Engineering
Hopf bifurcation
Hunting
Maturation
Mechanical Engineering
Predation
Predator-prey simulation
Predators
Stability analysis
Switches
System dynamics
Vibration
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Summary:The classical prey-predator model assumes that prey species has no life history. But many species whose individuals have a life history with two classes, namely immature and mature. Since, immature prey can be easily captured by the predators because of their short life experiences and less activity, while predators make some extra effort to catch mature prey. So, in this paper, a mathematical model is proposed to study the complex behaviour of a delayed prey-predator system with stage in prey population. We have included a maturation delay which is the time required for immature prey to join mature class and a cooperative hunting delay which is the time taken by predator to cooperate and attack on prey. Stability analysis has been addressed with different pairs of delays. Hopf bifurcation analysis with its directions is also performed. Global stability of predator free equilibrium point has been examined analytically and shown graphically. Both maturity and cooperative hunting delay significantly influence the system dynamics and produce multi-times stability switches. The presence of cooperative hunting delay of predators reduces the maturation time of prey due to which prey becomes mature very fast. Increase in cooperative hunting rate of predators suppress mature prey populations. Numerical simulations have been performed in various ways to support our theoretical findings.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-024-09923-y