Paper Info
Title
Discrete-time dynamics of a system with crowding effect and predator partially dependent on prey.
Abstract
In the present study, the stability and bifurcation analysis of discrete-time predator-prey system with predator partially dependent on prey and crowding effect of predator is examined. Global stability of the system at the fixed points has been discussed. The specific conditions for existence of flip bifurcation and Hopf bifurcation in the interior of R + 2 have been derived by using a center manifold theorem and bifurcation theory. Numerical simulations have been carried out to show the complex dynamical behavior of the system and to justify our analytic results. In case of flip bifurcation, numerical simulations presented cascade of period-doubling bifurcation in the orbits of period 2, 4, 8, chaotic orbits and stable window of period 9 orbit; whereas in case of Hopf bifurcation, smooth invariant circle bifurcates from the fixed point. The complexity of dynamical behavior is confirmed by computation of Lyapunov exponents.
Year
DOI
Venue
2015
10.1016/j.amc.2014.12.021
Applied Mathematics and Computation
Keywords
Field
DocType
lyapunov exponent,hopf bifurcation
Period-doubling bifurcation,Bogdanov–Takens bifurcation,Infinite-period bifurcation,Biological applications of bifurcation theory,Mathematical analysis,Bifurcation diagram,Transcritical bifurcation,Pitchfork bifurcation,Saddle-node bifurcation,Mathematics
Journal
Volume
Issue
ISSN
252
C
0096-3003
Citations 
PageRank 
References 
2
0.47
5
Authors
3
Name
Order
Citations
PageRank
Joydip Dhar13712.11
Harkaran Singh230.85
Harbax Singh Bhatti331.18