Spatiotemporal evolution in a (2+1)-dimensional chemotaxis model

Santo Banerjee, Amar P. Misra and L. Rondoni

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 1, 107-112

Abstract: Simulations are performed to investigate the nonlinear dynamics of a (2+1)-dimensional chemotaxis model of Keller–Segel (KS) type, with a logistic growth term. Because of its ability to display auto-aggregation, the KS model has been widely used to simulate self-organization in many biological systems. We show that the corresponding dynamics may lead to steady-states, to divergencies in a finite time as well as to the formation of spatiotemporal irregular patterns. The latter, in particular, appears to be chaotic in part of the range of bounded solutions, as demonstrated by the analysis of wavelet power spectra. Steady-states are achieved with sufficiently large values of the chemotactic coefficient (χ) and/or with growth rates r below a critical value rc. For r>rc, the solutions of the differential equations of the model diverge in a finite time. We also report on the pattern formation regime, for different values of χ, r and of the diffusion coefficient D.

Keywords: Spatio-temporal chaos; Chemotaxis model; Pattern formations; Wavelet spectra (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:1:p:107-112

DOI: 10.1016/j.physa.2011.07.053

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