Statistical neurodynamics of the oscillatory circuit underlying central pattern generation

On the basis of the statistical neurodynamics proposed by W.A. Little (1974). G.L. Shaw (1974), and J.W. Clark (1988) and the mathematical method of Markov chains with continuous time parameter, a study is presented on the statistical time development of asymmetric neuronal networks at the level of statistical mechanics. The method is used to analyze and simulate the central pattern generator (CPG) controlling escape swimming in the marine mollusc Tritonia diomedea The results provide support for the following conclusions: (1) there are some stochastic factors in CPG; (2) the collective output of CPG depends on the pattern of connection, the neuronal threshold, and excitability; (3) the rhythmic activity of Tritonia CPG is one cyclic sequence of period 4 (the stay-time parameter of every state is defined exactly); and (4) Markov chain theory can provide a general theoretical framework for understanding the retrieval dynamics of spatiotemporal patterns in biological neural networks and has a visible and concise mathematical treatment