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Oscillatory Turing patterns in network-organized reaction-diffusion systems
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.