Dynamics of coupled generators of quasiperiodic oscillations: Different types of synchronization and other phenomena

Кузнецов, А. П.; Кузнецов, С. П.; Shchegoleva, Natal’ya; Stankevich, Nataliya

doi:10.1016/j.physd.2019.05.014

Cited by 30 publications

(41 citation statements)

References 56 publications

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“…The possible number of representations of the task "x of x" is equal to the number of combinations x out of 16 (C x 16 ). Therefore, the highest probability to find a solution is for x = 8, and the smallest probability is for x = 16 at C 16 16 = 1 (see Figure 10). However, as it will be shown in the results, the type of distribution of the found solutions differs significantly from the distribution in Figure 10 and is determined by the network parameters.…”

Section: High Order Synchronizationmentioning

confidence: 99%

“…However, as it will be shown in the results, the type of distribution of the found solutions differs significantly from the distribution in Figure 10 and is determined by the network parameters. The total number of options for presenting tasks "x of x" is C x 16 + 1 = 2 16 = 65536, where the absence of synchronization with any input data is taken into account. The total number of network response options is much higher if we take into account answers of the type "n of x".…”

Section: High Order Synchronizationmentioning

confidence: 99%

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A Method for Evaluating Chimeric Synchronization of Coupled Oscillators and Its Application for Creating a Neural Network Information Converter

Velichko

2019

Electronics

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This paper presents a new method for evaluating the synchronization of quasi-periodic oscillations of two oscillators, termed “chimeric synchronization”. The family of metrics is proposed to create a neural network information converter based on a network of pulsed oscillators. In addition to transforming input information from digital to analogue, the converter can perform information processing after training the network by selecting control parameters. In the proposed neural network scheme, the data arrives at the input layer in the form of current levels of the oscillators and is converted into a set of non-repeating states of the chimeric synchronization of the output oscillator. By modelling a thermally coupled VO2-oscillator circuit, the network setup is demonstrated through the selection of coupling strength, power supply levels, and the synchronization efficiency parameter. The distribution of solutions depending on the operating mode of the oscillators, sub-threshold mode, or generation mode are revealed. Technological approaches for the implementation of a neural network information converter are proposed, and examples of its application for image filtering are demonstrated. The proposed method helps to significantly expand the capabilities of neuromorphic and logical devices based on synchronization effects.

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Section: High Order Synchronizationmentioning

confidence: 99%

Section: High Order Synchronizationmentioning

confidence: 99%

A Method for Evaluating Chimeric Synchronization of Coupled Oscillators and Its Application for Creating a Neural Network Information Converter

Velichko

2019

Electronics

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“…В то же время она представляет фундаментальный интерес. Два связанных квазипериодических генератора исследованы в работе [9]. Они демонстрируют достаточное количество интересных феноменов, включая эффект гибели колебаний, синхронную квазипериодичность и др.…”

Section: Introductionunclassified

Два Связанных Квазипериодических Генератора, Возбуждаемых Гармоническим Сигналом

Кузнецов¹,

Седова²,

Станкевич³

2021

Журнал Технической Физики

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A system of two dissipatively coupled generators, which can exhibit autonomous quasiperiodic oscillations, excited by a harmonic signal, is studied. Lyapunov charts are presented that reveal the regimes of invariant tori of different dimensions and chaos. Phase portraits in stroboscopic section and double Poincare section are presented. The coexistence of different regimes, in particular, the bifurcations of invariant tori, is discussed.

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“…In recent years there has been considerable interest in the study of multi-frequency quasiperiodic oscillations [1][2][3][4][5][6][7][8][9][10][11][12][13]. Such phenomena are widespread in nature and technology, in almost all areas of physics (radiophysics, electronics, laser physics, astrophysics, and many others), as well as in biology, chemistry, and medicine (see the above papers as well as monographs [14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

On two-frequency quasi-periodic perturbations of systems close to two-dimensional Hamiltonian ones with a double limit cycle

Kostromina

2021

Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki

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The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit cycle. Its solution is important both for the theory of synchronization of nonlinear oscillations and for the theory of bifurcations of dynamical systems. In the case of commensurability of the natural frequency of the unperturbed system with frequencies of quasi-periodic perturbation, resonance occurs. Averaged systems are derived that make it possible to ascertain the structure of the resonance zone, that is, to describe the behavior of solutions in the neighborhood of individual resonance levels. The study of these systems allows determining possible bifurcations arising when the resonance level deviates from the level of the unperturbed system, which generates a double limit cycle in a perturbed autonomous system. The theoretical results obtained are applied in the study of a two-frequency quasi-periodic perturbed pendulum-type equation and are illustrated by numerical computations.

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Dynamics of coupled generators of quasiperiodic oscillations: Different types of synchronization and other phenomena

Cited by 30 publications

References 56 publications

A Method for Evaluating Chimeric Synchronization of Coupled Oscillators and Its Application for Creating a Neural Network Information Converter

A Method for Evaluating Chimeric Synchronization of Coupled Oscillators and Its Application for Creating a Neural Network Information Converter

Два Связанных Квазипериодических Генератора, Возбуждаемых Гармоническим Сигналом

On two-frequency quasi-periodic perturbations of systems close to two-dimensional Hamiltonian ones with a double limit cycle

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