Pattern formation and Turing instability in an activator–inhibitor system with power-law coupling

F.A. dos S. Silva, R.L. Viana and S.R. Lopes

Physica A: Statistical Mechanics and its Applications, 2015, vol. 419, issue C, 487-497

Abstract: We investigate activator–inhibitor systems in two spatial dimensions with a non-local coupling, for which the interaction strength decreases with the lattice distance as a power-law. By varying a single parameter we can pass from a local (Laplacian) to a global (all-to-all) coupling type. We derived, from a linear stability analysis of the Fourier spatial modes, a set of conditions for the occurrence of a Turing instability, by which a spatially homogeneous pattern can become unstable. In nonlinear systems the growth of these modes is limited and pattern formation is possible. We have studied some qualitative features of the patterns formed in non-local coupled activator–inhibitor systems described by the Meinhardt–Gierer equations.

Keywords: Reaction–diffusion systems; Activator–inhibitor systems; Non-local couplings; Pattern formation; Spatio-temporal dynamics (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:419:y:2015:i:c:p:487-497

DOI: 10.1016/j.physa.2014.09.059

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