Contraction-Based Identification of a Neuron Model with Nonlinear Parameterization via Synchronization

In this work, a scheme for the identification of a nonlinearly parameterized neural system described by the Hindmarsh-Rose model, using synchronization and contraction for stability, is proposed. The given algorithm is based on the construction of an adaptive law which helps to render contractive, in a generalized sense, certain virtual system. This virtual dynamics is obtained as an abstract model for which the ideal identification goals and the identification error of the system under study are particular solutions. Contraction ensures that ideal and real trajectories tend to each other whenever they are initialized within the contraction region.The algorithm was successfully applied to identify the scalar nonlinear parameter of the Hindmarsh-Rose model and numerical results are shown in order to demonstrate the effectiveness of the method.