Abstract
The brain displays complex dynamics, including collective oscillations, and extensive research has been conducted to understand their generation. However, our understanding of how biological constraints influence these oscillations is incomplete. This study investigates the essential properties of neuronal networks needed to generate oscillations resembling those in the brain. A simple discrete-time model of interconnected excitable elements is developed, capable of closely resembling the complex oscillations observed in biological neural networks. In the model, synaptic connections remain active for a duration exceeding individual neuron activity. We show that the inhibitory synapses must exhibit longer activity than excitatory synapses to produce a diverse range of the dynamical states, including biologically plausible oscillations. Upon meeting this condition, the transition between different dynamical states can be controlled by external stochastic input to the neurons. The study provides a comprehensive explanation for the emergence of distinct dynamical states in neural networks based on specific parameters.