Synchronization control of two coupled non-identical hindmarsh-rose systems

The problem of controlled synchronization between two coupled non-identical Hindmarsh-Rose systems, each of which describes the behavior of a biological neuron, was considered. The importance of solving this problem is caused by a variety of medical and biological research that determines the correlation between the certain diseases of the nervous system (such as epilepsy) and pathological synchronization between neurons in the brain areas. Thus, the ability to control synchronization between neurons is a promising method for the therapy of epilepsy and has been actively used in medical practice. Obviously, the development of this method of therapy requires the usage of qualitative mathematical tools. Our approach is based on the applying of the tools of control theory. In addition, it is necessary to take into account an inaccuracy of the modern neural models. In order to do this, we propose to consider this inaccuracy in the form of the continuous functions which describe the disturbances. Thus, using the control law, which was suggested in this article, and abiding by the theorems, which were formulated here, it is possible to achieve synchronized behavior of the systems in the conditions of absence and presence of the disturbances. The results were proved and confirmed by simulations.