Entrainment and Modulation of Turing Patterns under Spatiotemporal Forcing

Hiroto Shoji^1,2

¹Kyoto Prefectural University of Medicine, Nishi-takatukasa 13, Kyoto 603-8334, Japan
²PRESTO, Japan Science and Technology Agency, 4-1-8, Honcho, Kawaguchi, Saitama 332-0012, Japan
E-mail address: shoji@koto.kpu-m.ac.jp

(Received November 29, 2008; Accepted January 17, 2009)

Abstract. We examine the time-evolutional behavior of self-organized Turing patterns under spatiotemporal forcing in one-dimensional systems. Based on the model equations, we apply a space-time-dependent external force. The entrainment and modulation of time-evolutional patterns are investigated numerically in one dimension. We develop a theoretical analysis to understand the obtained dynamics, and conjecture about the mode selection of the one-dimensional Turing pattern.

Keywords: Reaction-diffusion System, Turing, External Forcing, Phase Equation