Research on the relationship between controller emergent rhythms and biological oscillator

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In traditional artificial neural networks, the neuron behavior is described only in terms of firing rate, while most real neurons, commonly known as spiking neurons, transmit information by pulses, also called action potentials or spikes. We have presented three adaptive observers for a single neuron with the membrane potential measurement under the assumption that some of parameters in the HR neuron are known. Using the Kalman-Yakubovich lemma, we have shown the asymptotic stability of the error systems based on the standard adaptive control theory\cite{narendra}. The estimators allow us to recover the internal states and to distinguish the firing patterns with early-time dynamic behaviors.