Relationship Between the Nonlinear Oscillator and the Motor Cortex

The investigations show that the fractional calculus could be employed for complex biological systems and capture intrinsic phenomena. At the same time, the research results also show that the neural network has the characteristics of fractional calculus and its neuronal dynamics is complex. As a micro-neural circuit placed in the spinal cord, the central pattern generator (CPG) is supposed to have the property of fractional calculus. In order to study the application of the fractional order technique to the CPG, the fractional order CPG model is established based on the Matsuoka model. The stable conditions are given through mathematical analysis. In order to extract the relation between the motor cortex and the fractional order CPG, the coupling model between the fractional order CPG and the neural mass model (NMM) simulated the motor cortex is built. Moreover, the effects of coupling model parameters variations on the CPG and the NMM are investigated. The main findings are: first, the CPG output obtained with the fractional order is more accurate than the one obtained with the integral order. Increasing the fractional order makes the CPG output more accurate. Second, the results show that the motor cortex has corresponding modes with those of the CPG. And the NMM mode can switch in accordance with the change of fractional order. Third, the simulations also show that a new stable state in motor cortex could be produced based on the existing modes with the introduction of the fractional order CPG model. It can provide a helpful method to understand the working principles of the motor cortex.