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Chaos. 2019 Jan;29(1):013145. doi: 10.1063/1.5086909.

Mathematical modeling and analysis of two-variable system with noninteger-order derivative.

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Institute 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.
FST Errachidia Université Moulay Ismail, Meknes, Morocco.


The aim of this paper is to apply the newly trending Atangana-Baluanu derivative operator to model some symbiosis systems describing commmensalism and predator-prey processes. The choice of using this derivative is due to the fact that it combines nonlocal and nonsingular properties in its formulation, which are the essential ingredients when dealing with models of real-life applications. In addition, it is only the Atangana-Baleanu derivative that has both Markovian and non-Markovian properties. Also, its waiting time takes into account the power, exponential, and Mittag-Leffler laws in its formulation. Mathematical analysis of these dynamical models is considered to guide in the correct use of parameters therein, with chaotic and spatiotemporal results reported for some instances of fractional power α.


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