Modelling the Multiteam Prey–Predator Dynamics Using the Delay Differential Equation (original) (raw)
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In this article a system of retarded differential equations is proposed as a predator-prey model. We investigate the model, representing a resource (prey) and a two predator system with delay due to gestation. The response function is assumed here to be concave in nature. Since global stability of positive equilibrium is of great interest, we provide sufficient conditions in terms of parameters of the system to guarantee it. By the simulation process the bifurcation occurring are discussed in terms of two bifurcation parameters. We have also shown that the time delay can cause a stable equilibrium to become unstable and even switching of stabilities. Numerical simulations are given to illustrate the results. To cite this article:
Bifurcation in Coupled Predator-Prey Model with Time Delay
Hopf Bifurcation occurs when a periodic solution or limit cycle, surrounding an equilibrium point, arises or goes away as the bifurcation parameter is varied. Predator- prey systems are known to have periodic solutions. We find the conditions under which these periodic solutions will disappear as the bifurcation parameter (time delay) is varied.
Chaos, Solitons & Fractals, 2013
This paper concerns with a new delayed predator-prey model with stage structure on prey, in which the immature prey and the mature prey are preyed by predator and the delay is the length of the immature stage. Mathematical analysis of the model equations is given with regard to invariance of non-negativity, boundedness of solutions, permanence and global stability and nature of equilibria. Our work shows that the stage structure on the prey is one of the important factors that affect the extinction of the predator, and the predation on immature prey is a cause of periodic oscillation of population and can make the behaviors of the system more complex. The predation on the immature and mature prey brings both positive and negative effects on the permanence of the predator, if ignore the predation on immature prey in the system, the stage-structure on prey brings only negative effect on the permanence of the predator.