Quorum sensing via static coupling demonstrated by Chua's circuits

Abstract

Dynamical quorum sensing, the population based phenomenon, is believed to occur when the elements of a system interact via dynamic coupling. In the present work, we demonstrate an alternate scenario, involving static coupling, that could also lead to quorum sensing behavior. These static and dynamic coupling terms have already been employed by Konishi [Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, 2781 (2007)]. In our context, the coupling is defined as static or dynamic, on the basis of the relative time scales at which the surrounding dynamics and the elements' dynamics evolve. According to this, if the variation in the surrounding dynamics happens on a much larger (fast) time scale than that at which the elements' dynamics are varying (such as seconds and μs), then the coupling is considered to be static, otherwise it is considered to be dynamic. A series of experiments have been performed starting from a system of three Chua's circuits to a system of 20 Chua's circuits to study two types of quorum transitions: the emergence and the extinction of global oscillations (period-1). The numerics involving up to 100 Chua's circuits validate the experimental observations.