Coupling relationship between the central pattern generator and the cerebral cortex with time delay.

Brain activity is a cooperative process among neurons and involves the coupling relationship, which is crucial to perform operational tasks in various specialized areas of the nervous system. A finite signal transmission speed along the axons results in a space-dependent time delay. The central pattern generator (CPG) can in principle produce basic locomotor rhythm in the absence of inputs from higher brain centers and peripheral sensory feedback. To study the dynamic performance of CPG with time delay and its coupling relationship with the cerebral cortex, a new CPG model with time delay and a model of the neural mass model (NMM) and the CPG are developed. The coupling model is based on biological experimental results. Bifurcation theories and maximal Lyapunov exponent are used to analyze the dynamic performance. From the results, some CPGs are suggested to be embedded in limbs and composed of the parameters space which corresponds to the one of the cerebral cortex. This embodiment of humans can reduce the burden of the brain and simplify the control of the locomotion. The results also show that the phase diagram of the CPG cannot keep the limit cycle, and that the state of the NMM becomes increasingly chaotic as time delay increases. This finding implies that a person with slow reaction can easily lose the stability of his or her locomotion.