Chaotic Synchronization of Hindmarsh-Rose Neurons Coupled by Cubic Nonlinear Feedback

The chaotic synchronization of two cubic nonlinear coupling Hindmarsh-Rose (HR) neurons is discussed. A nonlinear coupling feedback term with higher order form of membrane potential is studied, and adds it to different position of the HR equation. Numerical simulation shows when the cubic nonlinear coupling feedback term only added to the first differential equation, in a quite large region of coupling strength, the two neurons cannot achieve full synchronization, On this condition, if the square form of membrane potential added to the second differential equation, the two neurons can achieve full synchronization in special coupling strength region. The synchronization stability has been proved by the calculation of the maximum conditional Lyapunov exponent. This investigation proposes the harmony theory of complex neuron network to some extent and provides it theoretical foundation for next step of research.