Coupling Relationships between the Brain and the Central Pattern Generator Based on a Fractional-Order Extended Hindmarsh-Rose Model.

Abstract

The states of the central nervous system (CNS) can be classified into subcritical, critical, and supercritical states that endow the system with information capacity, transmission capabilities, and dynamic range. A further investigation of the relationship between the CNS and the central pattern generators (CPG) is warranted to provide insight into the mechanisms that govern the locomotion system. In this study, we established a fractional-order CPG model based on an extended Hindmarsh-Rose model with time delay. A CNS model was further established using a recurrent excitation-inhibition neuronal network. Coupling between these CNS and CPG models was then explored, demonstrating a potential means by which oscillations generated by a neural network respond to periodic stimuli. These simulations yielded two key sets of findings. First, frequency sliding was observed when the CPG was sent to the CNS in the subcritical, critical, and supercritical states with different external stimulus and fractional-order index values, indicating that frequency sliding regulates brain function on multiple spatiotemporal scales when the CPG and CNS are coupled together. The main frequency range for these simulations was observed in the gamma band. Second, with increasing external inputs the coherence index for the CNS decreases, demonstrating that strong external inputs introduce neuronal stochasticity. Neural network synchronization is then reduced, triggering irregular neuronal firing. Together these results provide novel insight into the potential mechanisms that may underlie the locomotion system.