ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kuznetsov A. P., Seliverstova E. S., Trubetskov D. I., Turukina L. V. Phenomenon of the van der pol equation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, vol. 22, iss. 4, pp. 3-42. DOI: 10.18500/0869-6632-2014-22-4-3-42

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Russian
Heading: 
Review of Actual Problems of Nonlinear Dynamics
Article type: 
Review
UDC: 
517.91, 517.938, 51.73
DOI: 
10.18500/0869-6632-2014-22-4-3-42

Phenomenon of the van der pol equation

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Seliverstova Ekaterina Sergeevna, Saratov State University
Trubetskov Dmitriy Ivanovich, Saratov State University
Turukina L. V., Saratov State University
Abstract: 

This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radio­engineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his  name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters.
• The biography of van der Pol, history of his equation and supposed precursors.
• The contribution of A.A. Andronov in the theory of self­oscillations.
• Van der Pol equation and modeling of processes in the human body (the mode of the heart beat and of the «heart–vessels» system; modeling of processes in the large intestine; models of excitatory and inhibitory neural interactions; modeling synchronization in processing and transfer of information in neural networks; various problems related to human musculoskeletal apparatus; modeling the vocal cords).
• Development and modifications of the van der Pol equation.

Key words: 
Van der Pol equation
oscillations
biophysics
vacuum­tube oscillator
Neuron
synchronization
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Received: 
11.07.2014
Accepted: 
11.07.2014
Published: 
31.12.2014
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