Dynamical behavior of the firings in a coupled neuronal system

The time-interval sequences and the spatiotemporal patterns of the firings of a coupled neuronal network are investigated in this paper. For a single neuron stimulated by an external stimulus I, the time-interval sequences show a low-frequency firing of bursts of spikes and a reversed period-doubling cascade to a high-frequency repetitive firing state as the stimulus I is increased. For two neurons coupled to each other through the firing of the spikes, the complexity of the time-interval sequences becomes simple as the coupling strength increases. A network with a large number of neurons shows a complex spatiotemporal pattern structure. As the coupling strength increases, the number of phase-locked neurons increases and the time-interval diagram shows temporal chaos and a bifurcation in the space. The dynamical behavior is also verified by the behavior of the Lyapunov exponent.