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Astrocyte cells, the most existing abundant cells in central nervous system, play an essential role in modulating the neuronal activities, information processing, and regulating the synaptic plasticity through calcium (Ca2+) fluctuations of ions hemostasis by using a feedback mechanism. The pathophysiological and hypersynchronous neuronal activity can lead to the epileptic seizures, which is known as one of the neurodegenerative disorders in the field of neuroscience. This paper presents a modified neuron-astrocyte interaction (tripartite synapse) model based on leaky and integrate fire neuron and the astrocyte-synapse models using an area-efficient hardware approach called stochastic computing paradigm. The proposed model is synthesized physically on field-programmable gate array as a proof of concept. The implementation results of the presented model can mimic the bidirectional communication in biological minimal network of pre-postsynaptic and Ca2+-based model for astrocyte with considerably lower hardware cost. The influence of astrocytes on neural network behavioral has been investigated by providing a proper feedback mechanism and considering the role of gap junction coupling and the various coefficients on desynchronizing the impaired synchronization of the coupled neurons.