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Irregular brain activity is of interest to researchers and scientists who are trying to understand, model, compare, and provide novel solutions to existing and challenging issues. Neurological disorders such as epilepsy, Alzheimer’s disease, Parkinson’s disease, and schizophrenia have been extensively studied. Among those diseases, epileptic seizures are the most commonly occurring ones. In this work, as a simplification of the complete biological operations of the brain, it was viewed as a system that consists of coupled oscillators. This allowed us to examine epilepsy as a pathological manifestation of the system. Emerging behaviors that arise from the spatiotemporal interactions of simple oscillators, namely, Chua’s Circuit, allowed us to observe how irregularities and changes to the coupling parameters of a neuromorphic network affect their synchronization and result in the emergence of epileptic activity. To achieve this, the characteristics of novel nanoelectronic devices, namely, memristors, have been exploited through their integration into two-dimensional crossbar arrays that offer the advantages of reprogrammability, low area, and low power consumption.