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JOURNALS // Izvestiya VUZ. Applied Nonlinear Dynamics // Archive

Izvestiya VUZ. Applied Nonlinear Dynamics, 2014, Volume 22, Issue 4, Pages 3–42 (Mi ivp242)

This article is cited in 2 papers

Phenomenon of the van der pol equation

A. P. Kuznetsova, E. S. Seliverstovab, D. I. Trubetskovb, L. V. Turukinac

a Saratov Branch, Kotel'nikov Institute of Radio-Engineering and Electronics, Russian Academy of Sciences
b Saratov State University
c Saratov Branch of the Institute of Radio Engineering and Electronics

Abstract: This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radio-engineering, 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 self-oscillations.
• Van der Pol equation and modeling of processes in the human body (the model 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.

Keywords: Van der Pol equation, oscillations, biophysics, vacuum-tube oscillator, neuron, synchronization.

UDC: 517.91, 517.938, 51.73

Received: 11.07.2014



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