Chimera States - A Brief Introduction by Rajarshi
Middya and A Roy Chowdhury* in Research & Development in Material Science_
Biological science
The
plethora of systems considered during the study of coupling between entities
exhibiting nonlinear behaviour has led to the emergence of a new field of study
encompassing biological science and mathematics, where the connectivity between
neurones proves to be a worthwhile quest. But this is not restricted only to
the above mentioned domains. In this respect, the one thing that interests the
scientific community at large is the random presence of synchrony and its
absence in a cluster of nonlinear systems. Any large scale complex network is
capable of exhibiting this phenomenon. First observed by Kuramoto et al. [1-3]
the phenomena mentioned here has got a very interesting name dating back to the
time of Homer. Chimera - a three headed fire-breathing monster having the head
of a lion, the body of a goat and the tail of a serpent - is the name given to
this phenomenon.
In
a population of interconnected nonlinear systems identical in nature, the
occurrence of chimera states can be indicated by simultaneous existence of
coherent and incoherent states amongst different clusters of the population.
The coherent oscillators have their phase locked and the incoherent ones are
desynchronised amongst each other. The basic idea behind it was that, since the
behaviour of the network as a whole cannot be termed as synchronous between its
elements and neither can be termed as asynchronous, the confusion created is
similar to that of a chimera as one cannot exactly classify the chimera as a
particular animal. It should be kept in mind that similar phenomenon can be
observed in the case of a population consisting of non-identical systems. But
there as the asynchronous nature is attributed to the in homogeneity of the
network, it cannot be termed as chimera. An example of the existence of chimera
state in a population of similar nodes is shown in Figure 1.
This
figure gives a superficial idea about how the chimera state might look like in
a neural network consisting of about eight hundred nodes. The abcissa in Figure
1a is the node index and the ordinate is the one of the state variables. As can
be seen, between the nodes three hundred and four hundred there is a continuum
of the state variable thus indicating that the nodes are in sync with each
other. This is further bolstered by the continuous line in Figure 1 showing
that their phases are locked. Now that we have given a brief glimpse of what
chimera states might look like in a homogeneous population of nonlinear
oscillators, we are ready to point towards certain field of research where this
concept has proven its use. This is given the next section.
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