NDLI: Dynamics and responses of a predator–prey system with competitive interference and time delay

Content Provider	Springer Nature Link
Author	Upadhyay, Ranjit Kumar Agrawal, Rashmi
Copyright Year	2015
Abstract	In this paper, we have pointed out a time-delayed predator–prey system with modified Leslie–Gower and Beddington–DeAngelis type functional responses. We discuss the structure of nonnegative equilibria and their stability analysis. Also, the invariance and boundedness of the model system are investigated. It is observed that delay destabilizes the system when the value of delay crosses its critical value. When the delay parameter is taken equals to its critical value, Hopf bifurcation occurs. Conditions for the system to become globally asymptotically stable at nonzero equilibria are also obtained. By applying the normal form theory and center manifold theorem, stability, direction, and period of bifurcating solutions of the model system are calculated. It is observed that supercritical Hopf bifurcation occurs for a set of parameter values, and the bifurcating periodic solutions are stable with decreasing period. Following the global Hopf bifurcation result of Wu (Trans Am Math Soc 35:4799–4838, 1998) for functional differential equations, we have shown that the local Hopf bifurcation implies the global Hopf bifurcation. The theoretical results are justified by presenting some numerical simulations.
Starting Page	821
Ending Page	837
Page Count	17
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	83
Issue Number	1-2
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-09-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Predator–prey Beddington–DeAngelis functional response Time delay Hopf bifurcation Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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