Chaos Synchronization Of Neurons Via Active Disturbance Rejection Control

Since the phenomenon of chaos and chaos synchronization was found, it has been one of the fundamental research directions of nonlinear science, and it has been applied to many fields, such as physics, biology, information science, etc. In recent years, with the rapid development of neuroscience, scholars have found that the chaos synchronization method may reveal the process of information transmission between neurons. As a result, it is a research focus to apply the method of chaos synchronization to neuroscience.In this thesis, the active disturbance rejection controller is applied to achieve the chaos synchronization of coupling Duffing system, coupling cable neuron models and HR system, respectively. And the structure of this thesis is the following: firstly, a detailed analysis of the compositions of controller as well as their own functions is given and the effect of the coupling coefficient on chaos synchronization of Duffing system is studied, which reveals that the synchronization will not appear until the coupling coefficient satisfies some condition. When the condition stated above is not meet, an active disturbance rejection controller is added to the system. Secondly, the dynamics of single cable neuron under an applied electric field is studied and to better judge the status of neuron, the method of Lyapunov exponent is introduced. For coupling cable neuron model, the effect on synchronization of coupling strength is also discussed, and a controller is added to a weak coupling cable neuron system to achieve its synchronization. Finally, the chaos synchronization between two non-coupled HR neurons is considered. When one controller is applied to system, the single-variable chaotic synchronization will be achieved. However, when two controllers are added, the complete synchronization will appear.All the simulation results verify the effectiveness of the proposed strategy. Besides, it can be seen that the same active disturbance rejection controller can be applied to different models, and the controlling performance will remain the same with the parameters of controller varying in a wide range. Thus, the active disturbance rejection controller has strong adaptability and robustness.