Period-Halving Bifurcation of a Neuronal Recurrence Equation
نویسنده
چکیده
The sequences generated by neuronal recurrence equations of the form xHnL ! 1A⁄j!1 h aj xHn jL qE are studied. From a neuronal recurrence equation of memory size h that describes a cycle of length rHmLä lcmIp0, p1, ... , p-1+r HmLM, a set of rHmL neuronal recurrence equations is constructed with dynamics that describe respectively the transient of length OHrHmLä lcmHp0, ... , pdLL and the cycle of length OIrHmLä lcmIpd+1, ... , p-1+rHmLMM if 0 § d § -2 + rHmL and 1 if d ! rHmL 1. This result shows the exponential time of the convergence of the neuronal recurrence equation to fixed points and the existence of the period-halving bifurcation.
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