Frequency Synchronization and Its Possible Role in Microworld Phenomena
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PICAL ISSUE
Frequency Synchronization and Its Possible Role in Microworld Phenomena I. I. Blekhman Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, St. Petersburg, Russia e-mail: [email protected] Received July 23, 2019 Revised September 24, 2019 Accepted January 30, 2020
Abstract—We note the active interest of Yu.I. Neimark for research of frequency synchronization, as well as his substantial support for research in this area. In this work we discuss the main, not yet fully established, definitions and concepts of the theory of frequency synchronization. We consider significant differences between the phenomena of synchronization, self-synchronization, and entrainment. We emphasize that self-synchronization belongs to the class of self-organization phenomena, which is often ignored. We list some relevant unsolved problems of the theory of frequency synchronization, among them being the question of the possible fundamental role of synchronization in the microworld, which is discussed in detail. We express an opinion that it is advisable to attempt to describe physical reality by unified deterministic laws of physics, taking into account other new achievements in nonlinear dynamics listed in this work. Keywords: synchronization, self-synchronization, entrainment, tendency for synchronization, self-organization, synergetics, stability, quantization, universality, microworld phenomena, unsolved problems DOI: 10.1134/S0005117920080044
1. INTRODUCTION. Yu.I. NEYMARK AND SYNCHRONIZATION PROBLEMS Yuri Isaakovich Neimark was actively interested in the problem of frequency synchronization. A comprehensive publication [1] is devoted to this problem; see also [2]. Devoting these lines to the loving memory of Yuri Isaakovich, I would like to talk about several meetings with him that played a significant role in the development of works on synchronization and influenced my own scientific fate. My first acquaintance with Yu.I. Neimark dates back to the 1950–1960s. At the invitation of A.I. Lurie, Yuri Isaakovich spoke at a city seminar at the Leningrad Polytechnical Institute. It was an exciting and very interesting report on homoclinic structures. I remember that Yuri Isaakovich already spoke about the effects of complex (“chaotic”) behavior of simple dynamical systems, i.e., spoke about it earlier than the famous Lorentz article on a strange attractor appeared [3]. Lurie and other participants listened to the report with great attention and interest, there were many questions. The second memory refers to a later period. During a stay in Gorky on one of the thesis defenses, Yuri Isaakovich invited me to ride a boat along the Volga. During the trip, Yuri Isaakovich spoke in a free, relaxed form about various problems of the theory of nonlinear oscillations and, in particular, 1405
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about what should be attributed to nonlinear phenomena and about simple models of nonlinear phenomena. He suggested that, from a certain point of view, there are only four such phenomena: entrainment, sy
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