Abstract
Previous studies on the synchronization behaviors of neuronal networks were constructed by integer-order neuronal models. In contrast, this paper proposes that the above topics of symmetrical neuronal networks are constructed by fractional-order Hindmarsh–Rose (HR) models under electromagnetic radiation. They are then investigated numerically. From the research results, several novel phenomena and conclusions can be drawn. First, for the two symmetrical coupled neuronal models, the synchronization degree is influenced by the fractional-order q and the feedback gain parameter k1. In addition, the fractional-order or the parameter k1 can induce the synchronization transitions of bursting synchronization, perfect synchronization and phase synchronization. For perfect synchronization, the synchronization transitions of chaotic synchronization and periodic synchronization induced by q or parameter k1 are also observed. In particular, when the fractional-order is small, such as 0.6, the synchronization transitions are more complex. Then, for a symmetrical ring neuronal network under electromagnetic radiation, with the change in the memory-conductance parameter β of the electromagnetic radiation, k1 and q, compared with the fractional-order HR model’s ring neuronal network without electromagnetic radiation, the synchronization behaviors are more complex. According to the simulation results, the influence of k1 and q can be summarized into three cases: β>0.02, −0.06<β<0.02 and β<−0.06. The influence rules and some interesting phenomena are investigated.
Highlights
The firing behavior of neurons is a nonlinear process, and the neurons are a complex, nonlinear dynamic system
The synchronization behaviors and synchronization transitions of coupled fractional-order neuronal models and neuronal networks constructed by fractional-order HR neuronal models under electromagnetic radiation have not been investigated in previous studies
This paper investigates the synchronization behaviors and synchronization transitions of fractional-order neuronal networks under electromagnetic radiation
Summary
The firing behavior of neurons is a nonlinear process, and the neurons are a complex, nonlinear dynamic system. In 1952, Hodgkin and Huxley used equivalent circuits and large amounts of data from experiments to model and analyze the data, and they constructed the Hodgkin–Huxley (HH) neuron model through theoretical derivation [1]. Synchronization is an important phenomenon in the neuronal system and is one of the operational mechanisms of the brain. A number of researchers have used coupled neuronal models to try to explain some of the synchronization phenomena observed in experiments. Because the synchronization is related to neurological diseases in the brain, such as Parkinson’s disease [5] and epilepsy [6], investigating the synchronization behaviors of neuronal systems by theoretical methods or experiments is helpful to understand the mechanisms of related phenomena
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