Oscillatory Turing patterns in network-organized reaction-diffusion systems

Abstract:

Turing instability is one of the universal mechanisms of self-organized pattern formations in nature, which has been experimentally and theoretically investigated for chemical and biological reaction-diffusion media. Stationary patterns induced by the Turing instabillity have been considered also in network-organized systems and their properties for different kinds of random networks have been discussed. The Turing instability may induce not only stationary patterns but also time-dependent patterns. In the latter case of the oscillatory Turing instability, traveling wave patterns develop in continuous media.

In this talk, we present effects of pattern formation arising from the oscillatory Turing instability in network-organized systems. Instead of traveling waves, oscillatory patterns are spontaneously emerging in a subset of network nodes, depending on the network architecture, while the other nodes continue to rest in the stationary steady state. Our study reveals that oscillations may occur even though each individual node is not an oscillator, leading to a new scenario of oscillatory dynamics in network-organized systems.