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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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Phenomenon of the van der pol equation

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

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.

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