Complex System


Many complex systems, both natural and artificial, exhibit sychronization phenomena, which can be modeled using weakly coupled oscillators. Most previous studies focus on stability. Yet many complex systems (such as the human brain) do not converege on stable sychronized states. Rather they are metastable, temporarily dwelling in the vicinity of one stable state before migrating away from it towards another. A second feature of many complex systems (including the brain) is competition. In the context of sychronization, this is manifest in so-called chimera states, where one coalition of oscillators sychronizes whiile rival coalitions of identical oscillators are desychronized…………

Periodic phenomena involving the sychronizatiion of multiple variables are prevelant both in nature and the human eniviroment, and can be modeled mathmatically as systems of coupled oscillators……… A system that gives rise to these so-called chimera states is a plausible model for a competitive process wherein a set of winners forms alliance to the exclusion of the rest of the population. Since competitive processes of this sort dominate the dynamics of the brain, the economy, and the ecospehere, they are of considerable scientific interest.


Murray Shanahan, Metastable chimers states in community-structured oscillator networks

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