The dynamical analysis of non-uniform neocortical network model in up-down state oscillations

The brain is the most complex organ of the human body and consists of many excitatory and inhibitory neurons. The neural interactions are through synaptic connections. Such connections are the pathway of information; therefore, the neurons can exhibit various dynamical behaviors based on the active synapses. This paper employs a non-uniform neuronal network model of the brain neocortex to investigate the synchronization of up-down state oscillations. The dynamical analysis is performed using the bifurcation diagrams, Lyapunov exponents' spectra, phase portraits, and time series as a function of different coupling parameters. The results revealed that the studied model exhibits chaotic behavior in a wide range of the variation of the coupling strengths. Furthermore, when excitatory-excitatory neuronal coupling strength is assumed as the control parameter, some instantaneous periodic windows were detected within the chaotic regions, which is a rare phenomenon of neural dynamics.