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Synchronization of two Hindmarsh-Rose neurons with thresholds coupling

Luis Javier ontañón, Eric Campos Canton, Felipe Manuel Caballero Flores
The Hindmarsh-Rose (HR) dynamical system is a well-known model of neuronal activity. This work addresses chaotic dynamic synchronization of two HR neurons via coupling based on the thresholds. The coupling is unidirectional and it is carried out by an underdamped signal, which activates every time that the master system crosses the threshold represented by means of a Poincarè plane. A novel master-slave system is presented, and the synchronization between the systems is detected via the auxiliary system approach. Numerical explorations verify such synchronization where the parameters of two HR neurons might differ. The result gives away a fundamental question on the valid interpretation of unidirectional links, their potential use, and if such chaotic synchronization is an active principle of biological neurons.
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