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Linking Predation Risk, Herbivore Physiological Stress and Microbial Decomposition of Plant Litter
Published on: March 12, 2013
Computational study of noninteger order system of predation
1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa and Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria.
Abstract:
In this paper, we analyze the stability of the equilibrium point and Hopf bifurcation point in the three-component time-fractional differential equation, which describes the predator-prey interaction between different species. In the dynamics, the classical first-order derivative in time is modelled by either the Caputo or the Atangana-Baleanu fractional derivative of order α,0<α<1. We utilized a fractional version of the Adams-Bashforth formula to discretize these fractional derivatives in time. The results of the linear stability analysis presented are confirmed by computer simulation results.
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