We report the existence of phase-coupled oscillations in a model neural system. The model consists of a group of excitatory principal cells in interaction with local inhibitory interneurons. The voltages across the membranes of excitatory cells are governed primarily by calcium and potassium ion conductivities. The number of potassium channels open at any given instant changes in accordance with a deterministic law. The time scale of this change is set by a constant which depends on midpoint potentials at which potassium and calcium currents are half-activated. The growth of mean membrane potential of excitatory principal cells is controlled by that of the inhibitory interneurons. Nonlinear oscillatory system associated with these limit cycles starting from two different initial conditions maintain a definite phase relationship. The phase-coupled oscillations in electrical activity of the neuronal cells carry together amplitude, phase, and time information for cellular signaling. This mechanism supports an energy efficient way of information processing in the central nervous system. The information content is encoded as persistent periodic oscillations represented by stable limit cycles in the phase space. 1. Introduction The rhythmic oscillations are abundant in nature and they also exist at all levels of organization in the biotic world. The well-known examples are circadian rhythms [1], relaxation oscillations in heart beats [2, 3], and gene regulatory networks [4]. The electrical and magnetic activity of human brain has many oscillatory networks that coexist, and they perform unique physiological and cognitive functions. The frequency of oscillations in these networks is used to categorize them in different bands such as , , , and [5], and they characterize different physiological states. The oscillations in band represent eyes closed/relaxed states, the band is characteristic of eyes open, cognition is and alert state, during higher cognitive functioning, and is during sleep condition or under the action of anesthesia. These oscillations represent ongoing and spontaneous activities of the brain as under process by different neuronal organizations emerging from arrays of neuronal tissues and cells in the brain. The neuronal cells communicate with each other through action potentials as stated in electrophysiological parlance. These action potentials are rapid reversals in voltages across the plasma membrane of neuronal cells axons, mediated by voltage-gated ion channels [6]. Brain oscillatory networks play a key role in information processing, and
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