Turing bifurcation analysis for a predator-prey reaction-diffusion system
Department of Applied Mathematics and Statistics, Institute of Space and Technology Islamabad, Islamabad, 44000, Pakistan
2 Department of Space Science, Institute of Space and Technology Islamabad, Islamabad, 44000, Pakistan
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Accepted: 13 June 2017
Published online: 25 September 2017
In this article a physical model of predator-prey reaction-diffusion is considered. The Routh-Hurwitz stability criterion is used to analyze the stability of the dynamical system. Turing instability conditions are derived to investigate the Turing bifurcation. Stability conditions are used to get simulation results for the bifurcation diagram with the variation in diffusion. The effects of parameters, time delay and predator rate, are investigated on the nonlinear behavior of the system. Moreover, the chaotic behavior of the system is discussed through phase portraits and time history. The sensitive dependence of the system on the initial condition is presented graphically through time history maps.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, 2017