Abstract
Synchronization of biological neurons is not only a hot topic, but also a difficult issue in the field of bioelectrical physiology. Numerous reported synchronization algorithms are designed on the basis of neural model, but they have deficiencies like relatively complex and poor robustness and are difficult to be realized. Morris-Lecar neuron is considered, and linear active disturbance rejection control (LADRC) is designed. Only one control input signal is utilized to synchronize membrane potentials of biological neurons. Meanwhile, in order to verify the robustness of synchronization, sinusoidal signal and parameter perturbations are introduced in numerical simulations. LADRC can still achieve satisfactory synchronization. Both theoretical and numerical simulation results show that LADRC is capable of estimating and cancelling disturbances and uncertainties. Neither accurate neural models nor concrete disturbance signal models are indispensable. A more practical and effective thought is provided to address the synchronization between neurons.
Highlights
Complex and powerful biological nervous systems are composed of a great number of connected neurons
linear active disturbance rejection control (LADRC) is adopted to discuss the synchronization of Morris-Lecar neuronal membrane potentials
It has been analysed that LADRC can get asymptotic synchronization of neuronal membrane potentials by selecting appropriate parameters of extended state observer (ESO) and controller
Summary
Complex and powerful biological nervous systems are composed of a great number of connected neurons. Actualizing the synchronization of biological neurons has become a hot and difficult topic in bioelectricity physiology, nonlinear system theory, control, and many other areas. Based on the above models, in order to assist the abnormal nervous systems to operate normally, scholars from nonlinear control area began to study how to exert an external control signal, i.e., an external electrical stimulation, to drive different discharging modes between neurons to be synchronized. In order to reduce difficulty of parameter tuning, Gao proposed linear active disturbance rejection control (LADRC) and provided bandwidthparameterization based tuning method for LADRC [22]. The synchronization of Morris-Lecar neuronal membrane potentials is considered and LADRC is utilized to reject disturbance and achieve desired synchronization.
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