Abstract
This paper studies the chemical synaptic coupling of Chay neurons and the effect of adding time delay on their synchronization behavior. The results indicate that coupling strength stimuli can affect the discharge activity and the synchronization behavior. In the absence of coupling strength, the Chay neurons have chaotic discharge behavior and the system is in a nonsynchronous state. When a certain coupling strength is added, the neurons change from chaotic discharge to ordered periodic discharge, and the system state changes from asynchronous to synchronous. On the other hand, a time lag can alter the coupled system from synchronous to asynchronous.
Highlights
Synchronization is a common phenomenon in nonlinear dynamics [1]
It was discovered that neurological diseases such as Parkinson’s, trembling of the human hands, and epilepsy are caused by some morbid synchronization or non-synchronization [7,8,9]
The results showed that after applying the control, HH neurons could quickly track the dynamic behavior of the rest of the neurons
Summary
Synchronization is a common phenomenon in nonlinear dynamics [1]. In recent years, this phenomenon has received considerable attention due to its huge application prospects in chemistry, biology, physics, and information processing [2,3,4,5,6]. In order to study the nonlinear dynamic behavior and synchronization of single neurons and neural networks, researchers have established neuron mathematical models such as the Hodgkin–Huxley (HH), Morris–Lecar (ML), Hindmarsh–Rose (HR), FitzHugh–Nagumo (FHM), and the Chay representations. The Chay model was established in 1985 as a theoretical formulation with a high degree of uniformity based on different types of excitable cells playing an important role in Ca2+-related K+ channels, such as neurons, cardiomyocytes, and nerve endings. Li Hongming [29] studied the Chay neuron model under constant current stimulation based on the stability theory. In terms of chaotic motion, a time lag causes chaos in first-order nonlinear dynamical systems. Zheng Yanhong [31] discussed the influence of time delay on the synchronous dynamics of four ring-coupled chaotic HR neurons.
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