Global feedback control of Turing patterns in network-organized activator-inhibitor systems

¹ Department of Physics, Kyoto University - Kyoto, 606-8502, Japan
² JST CREST - Kyoto, 606-8502, Japan
³ Department of Mechanical and Environmental Informatics, Tokyo Institute of Technology - Tokyo, 152-8552, Japan
⁴ Abteilung Physikalische Chemie, Fritz-Haber-Institut der Max-Planck-Gesellschaft - Faradayweg 4-6, 14195 Berlin, Germany

^(a) hata@ton.scphys.kyoto-u.ac.jp

Received: 21 February 2012
Accepted: 30 May 2012

Abstract

Results of the first systematic study on feedback control of nonequilibrium pattern formation in networks are reported. Effects of global feedback control on Turing patterns in network-organized activator-inhibitor system have been investigated. The feedback signal was introduced into one of the parameters of the system and was proportional to the amplitude of the developing Turing pattern. Without the control, the Turing instability corresponded to a subcritical bifurcation and hysteresis effects were observed. Sufficiently strong feedback control rendered, however, the bifurcation supercritical and eliminated the hysteresis effects.