Numerical simulations of multilingual competition dynamics with nonlocal derivative

Kolade M. Owolabi and J.F. Gómez-Aguilar

Chaos, Solitons & Fractals, 2018, vol. 117, issue C, 175-182

Abstract: The dynamics of the language competition model is considered in this paper. The classical system is converted to non-integer order case by replacing the second-order partial derivative with the Riesz fractional derivative. A well-known numerical approximation methods based on the Fourier spectral algorithm in space and the third-order exponential time-differencing scheme are formulated to numerically simulate the three component fractional-in-space reaction-diffusion system in one and high dimensions for different values of α. Numerical results indicate α ∈ (1, 1.5] as the key control parameter that can influence the coexistence of various speakers over a period of time.

Keywords: Fractional calculus; Language competition; Exponential time integrator; Space-fractional reaction-diffusion; Numerical simulations; Riesz derivative (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:117:y:2018:i:c:p:175-182

DOI: 10.1016/j.chaos.2018.10.020

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