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An Isaac Newton Institute Workshop

Theory and Applications of Coupled Cell Networks


Author: Rabinovich M.I. (UCSD)


It is well known that the traditional way for neural computations is computation with attractors. This means transformation of a given input - an initial state inside of the basin of attraction of one attractor, to a fixed desired output. Five years ago Rabinovich et al. (2000) have introduced a new concept based on the Winnerless Competition (WLC) principle. According to this principle the incoming stimulus is transformed into a complex temporal output based on the intrinsic sequential dynamics of a network with WLC. They have shown that the neural circuits with non-symmetric inhibition demonstrate sequentially switching WLC dynamics that is stable and uniquely depends on the incoming information. The WLC principle is able to solve the contradiction between stability and flexibility in neural circuits. An appropriate set of mathematical models for competition phenomena is based on the generalized Lotka-Volterra models. These models describe the cooperative dynamics of an arbitrary number of competitive agents that can be dynamical elements themselves. Generally, the evolution of the system follows complicated or even chaotic trajectory in the phase space. In particular, the authors have analyzed the chaotic (strange attractor), periodic (limit cycle), and transient (Stable Heteroclinic Sequence (SHS)) cooperative sequential dynamics of simple and complex (random) networks. The transient sequential representation of the olfactory information (SHS) has been observed in the locust and bee’s antennal lobe. The interaction of excitatory and inhibitory neural ensembles in a model of brain microcircuits also leads to the SHS. The authors have also shown that the irregular hunting swimming of the marine mollusk Clione is the result of the chaotic dynamics of the gravimetric sensory network, consisting of interconnected inhibitory neurons (chaotic WLC).