A new biological central pattern generator model and its relationship with the motor units

The central pattern generator (CPG) is a key neural-circuit component of the locomotion control system. Recently, numerous molecular and genetic approaches have been proposed for investigating the CPG mechanisms. The rhythm in the CPG locomotor circuits comes from the activity in the ipsilateral excitatory neurons whose output is controlled by inter-neuron inhibitory connections. Conventional models for simulating the CPG mechanism are complex Hodgkin-Huxley-type models. Inspired by biological investigations and the continuous-time Matsuoka model, we propose new integral-order and fractional-order CPG models, which consider time delays and synaptic interfaces. The phase diagrams exhibit limit cycles and periodic solutions, in agreement with the CPG biological characteristics. As well, the fractional-order model shows state transitions with order variations. In addition, we investigate the relationship between the CPG and the motor units through the construction of integral-order and fractional-order coupling models. Simulations of these coupling models show that the states generated by the three motor units are in accordance with the experimentally-obtained states in previous studies. The proposed models reveal that the CPG can regulate limb locomotion patterns through connection weights and synaptic interfaces. Moreover, in comparison to the integral-order models, the fractional-order ones appear to be more effective, and hence more suitable for describing the dynamics of the CPG biological system.