Pattern control of external electromagnetic stimulation to neuronal networks

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ORIGINAL PAPER

Pattern control of external electromagnetic stimulation to neuronal networks Lianghui Qu · Lin Du Zichen Deng

· Haiwei Hu · Zilu Cao ·

Received: 19 June 2020 / Accepted: 4 November 2020 © Springer Nature B.V. 2020

Abstract The application of external electromagnetic stimulation to regulate the electrophysiological activities of specific brain regions can provide an ideal control or treatment scheme for some non-organic mental diseases. To further explore the effectiveness of electromagnetic stimulation in the treatment of mental illnesses, the regulatory abilities of external electromagnetic stimulation on the pattern dynamics of Newman– Watts small-world neuronal networks are systematically studied. The main stability function is used to construct four periodic or chaotic synchronous networks. Also, the average discharge frequency and the consistency coefficient are selected to measure the regulatory effects of external electromagnetic stimulation on the network dynamics. Numerical experiments show that electromagnetic stimulation can inhibit the electrophysiological activities of neuronal networks. Periodic electromagnetic stimulation with large amplitude or L. Qu · L. Du (B)· H. Hu · Z. Cao · Z. Deng School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, China e-mail: [email protected] Z. Deng School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710129, China L. Qu College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China L. Qu · L. Du · H. Hu · Z. Cao · Z. Deng MIIT Key Laboratory of Dynamics and Control of Complex Systems, Xi’an 710072, China

stochastic electromagnetic stimulation with large deviation has a more significant inhibitory effect on the discharge activities, not only effectively desynchronizing the discharge activities, but also controlling the evolution of spatiotemporal patterns, and even inducing the synchronization transition. Additionally, the number of stimulated neurons in neuronal networks also plays an important role in the evolution of spatiotemporal patterns. This study could provide theoretical guidance for the physiological application of electromagnetic stimulation in the treatment of certain mental diseases. Keywords Neuronal network · Electromagnetic stimulation · Main stability function · Synchronization transition · Pattern control

1 Introduction The human brain composed of nearly 100 billion neurons and a large number of glial cells has a very complex physiological structure, which is mainly responsible for the collection, integration, processing and transmission of neural information. Generally, different brain regions correspond to different physiological functions. Each neuron in the same brain region not only has relatively independent electrophysiological activities, but also interacts with each other to achieve common physiological function. Up to now, many practical mathematical models of neurons have been established [1–3], and the effects of som