Synchronization for fractional-order extended Hindmarsh-Rose neuronal models with magneto-acoustical stimulation input

Abstract

We investigate the generalized projective synchronization (GPS) problem of fractional-order extended Hindmarsh-Rose (FOEHR) neuronal models with magneto-acoustical stimulation input. The improved neuronal model has advantages in depicting the biological characteristics of neurons and therefore exhibits complex firing behaviors. In addition, we consider the nonlinearity and uncertain parameters of the neuronal model as well as the unknown external disturbances, which make the synchronization control of the master-slave neuron system more difficult. For the synchronous firing rhythms of neurons, a neural network (NN) sliding mode algorithm for the FOEHR neuron system is derived by the Lyapunov approach. We use a radial basis NN to approximate the unknown nonlinear dynamics of the error system, and the adaptive parameters are robust to the approximation errors, model uncertainties and unknown external disturbances. Under the proposed control scheme, the master and slave neuron systems can achieve GPS in a finite amount of time and realize resilience for the uncertain parameters and the external disturbances. The simulation results demonstrate that the membrane potentials of the slave neuron synchronize with those of the master neuron in proportion and that the underlying synchronization errors converge towards an arbitrarily small neighborhood of zero.