Abstract:
Turing instability in activator-inhibitor systems provides a paradigm of non-equilibrium self-organization; it has been extensively investigated for biological and chemical processes. However, Turing instability is also possible in networks. They have studied Turing patterns in large random networks. The initial linear instability leads to spontaneous differentiation of the network nodes into activator-rich and activator-poor groups. The emerging Turing patterns become, however, strongly reshaped at the subsequent nonlinear stage. Multiple coexisting stationary states and hysteresis effects are observed. This behaviour can be understood in the framework of a mean-field theory. Recently, control of network Turing patterns by application of global feedbacks has been investigated. Their results offer a new perspective in self-organization phenomena in systems organized as complex networks. Potential applications include ecological metapopulations, synthetic esosystem cellular networks of early biological morphogenesis, and networks of coupled chemical nanoreactors.

Prof. Mikhailov is a senior staff scientist and a researcher group leader in the Fritz Haber Institute since 1995. The group carries out theoretical research on a broad range of topics related to nonlinear self-organization phenomena in nonequilibrium chemical and biological systems. Current research interests are focused on modeling of protein machines, complex networks dynamics and problems related to the reactive soft matter.