Spatiotemporal evolution in a -dimensional chemotaxis model

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 r c . For r > r c , 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 .