Predefined-time synchronization of 5D Hindmarsh-Rose neuron networks via backstepping design and application in secure communication.

In this paper, the fast synchronization problem of 5D Hindmarsh-Rose neuron networks is studied. Firstly, the global predefined-time stability of a class of nonlinear dynamical systems is investigated under the complete beta function. Then an active controller via backstepping design is proposed to achieve predefined-time synchronization of two 5D Hindmarsh-Rose neuron networks in which the synchronization time of each state variable of the master-slave 5D Hindmarsh-Rose neuron networks is different and can be defined in advance, respectively. To show the applicability of the obtained theoretical results, the designed predefined-time backstepping controller is applied to secure communication to realize asynchronous communication of multiple different messages. Three numerical simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]