Synchronization criteria for delay coupled Izhikevich neurons

In this chapter, we investigate the chaotic synchronization of two coupled Izhikevich neurons via a gap junction. In the absence of a controller, the coupled neurons will achieve complete chaotic synchronization only when the degree of connectivity or the coupling strength exceeds a critical value. This transition to synchronization with varying connectivity strengths is analysed with conditional Lyapunov exponents. Synchronization of gap junction separated, coupled Izhikevich neurons using control laws has remained non-investigated to this date. As such, in this chapter we propose a nonlinear adaptive controller, in order to obtain complete chaotic synchronization for any value of coupling strength and delay, based on the Lyapunov stability theory. Effectiveness of the proposed nonlinear controller for synchronizing delayed-coupled Izhikevich neurons are shown through numerical simulations.