Abstract
In this work, we focus on both nonspatial and spatially extended predator–prey systems whose dynamics are described by the Holling type-IV functional responses. The classical time derivative in such models is replaced with the Atangana–Baleanu fractional derivative with nonlocal and nonsingular properties. A two-step scheme based on fractional Adams–Bashforth method is the formulation for the approximation of this derivative. We present a brief linear stability analysis for nondiffusive system and report Hopf and Turing bifurcation analysis for the spatial case. For different parameter values of \(\alpha \in (0,1]\), we obtain a range pattern results from numerical experiments. We also justify the difference between the integer and noninteger order results via numerical simulation.
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Owolabi, K.M. (2020). Numerical Simulation of Nonlinear Ecological Models with Nonlocal and Nonsingular Fractional Derivative. In: Dutta, H. (eds) Mathematical Modelling in Health, Social and Applied Sciences. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-2286-4_10
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DOI: https://doi.org/10.1007/978-981-15-2286-4_10
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