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We study the global dynamics of nonlinear networks made up of synchronous threshold elements. By writing a master equation for the system, we obtain an expression for the time dependence of its activity as a function of parameter values. We show that with both excitatory and inhibitory couplings, a network can display collective behavior which can be either multiple periodic or deterministic chaotic, a result that appears to be quite general.
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Choi et al. (1983) studied this question.
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