Chaotic synchronization and control in nonlinear-coupled Hindmarsh–Rose neural systems

A new approach for chaotic synchronization of Hindmarsh–Rose (HR) neural networks linked by special nonlinear coupling function is proposed. The method expands SC method in investigation of chaotic synchronization based on the stability criterion. We provide the error evolutional equation to determine the stability of synchronized states, which has very simple forms corresponding to matrix of star coupling coefficients. The synchronization can be achieved without the requirement to calculate the maximum Lyapunov exponents when the coupling strengths are taken as reference values, and there is a region of stability around them. Besides, the stability criterion control method is applied to control chaotic behaviors of individual Hindmarsh–Rose neuron model. The chaotic orbit is stabilized on 5spike/burst orbit embedded in the chaotic attractor by an input of the nonlinear time-continuous feedback perturbation to membrane potential.