Chaos Control And Synchronization Of Neurons

Biology system is a complex nonlinear system which has been proven that there exist chaotic characteristic from many aspects in recent years. Thus, whether and how we can use the chaos control to drive the biology system to the expected condition is a difficult and hot subject of the two interdisciplinary studies—nonlinear science and biomedicine science. The chaotic synchronization of signals among neurons plays the important role in the signal processing of neural system, so study of the neuron spiking and synchronization in neural system is the main content of neural science and the Chinese medicine modernization.In this paper, the classical neuron model Hodgkin-Huxley (HH) and FitzHugh–Nagumo (FHN) are chosen to be the main research objects. At first, the nonlinear dynamics of a single neuron under low frequency external electric field is studied in detail, and the coupled two-neurons HH system, the unidirectional-coupled two-neurons FHN system and the gap junction bidirectional-coupled two-neurons FHN system are established. Next, chaos control and synchronization theory is applied to study chaos synchronization of the active voltage transportation between neurons in external electric field. A nonlinear feedback linearization control scheme is proposed to synchronize the two-neurons system; considering the external perturbation and the parameter uncertainties, an adaptive control as well as an active control strategy is designed to synchronize two-neurons system; for the bidirectional-coupled FHN system, an improved MIMO decoupled feedback linearization and adaptive strategy is provided to synchronize all the state variables. Meanwhile, a multi-neurons coupled system is developed and a nonlinear control strategy is derived to synchronize the chaotic system. The theoretical analysis and the numerical simulations show the effectiveness of these proposed methods.These results can throw light on the researches of the brain and the quantitative analysis of acupuncture.