 Mathematical modelling and analysis of two-component system with Caputo fractional derivative orderKolade M. Owolabi Chaos, Solitons & Fractals, 2017, vol. 103, issue C, 544-554 Abstract: A class of generic spatially extended fractional reaction-diffusion systems that modelled predator-prey interactions is considered. The first order time derivative is replaced with the Caputo fractional derivative of order γ ∈ (0, 1). The local analysis where the equilibrium points and their stability behaviours are determined is based on the adoption of qualitative theory for dynamical systems ordinary differential equations. We derived conditions for Hopf bifurcation analytically. Most significantly, existence conditions for a unique stable limit cycle in the phase plane are determined analytically. Our analytical findings are in agreement with the numerical results presented in one and two dimensions. The system of fractional nonlinear reaction-diffusion equations has demonstrated the usefulness of understanding the dynamics of nonlinear phenomena. Keywords: Caputo derivative; Exponential integrator; Fractional reaction-diffusion; Hopf bifurcation; Oscillations; Predator-prey system; Stability analysis (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:103:y:2017:i:c:p:544-554 DOI: 10.1016/j.chaos.2017.07.013 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
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