Chaos via torus breakdown

Matsumoto, Takashi; Chua, Leon O.; Tokunaga, Ryuji

doi:10.1109/tcs.1987.1086135

Cited by 100 publications

(35 citation statements)

References 15 publications

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“…To examine this assumption we have considered the dynamics of two unidirectionally coupled Chua's circuits [31,32] with piecewise linear characteristic (see Fig. 4).…”

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confidence: 99%

Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

Hramov

Короновский

2005

Europhys. Lett.

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Abstract. -A new behavior type of unidirectionally coupled chaotic oscillators near the generalized synchronization transition has been detected. It has been shown that the generalized synchronization appearance is preceded by the intermitted behavior: close to threshold parameter value the coupled chaotic systems demonstrate the generalized synchronization most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous bursts. This type of the system behavior has been called intermitted generalized synchronization (IGS) by analogy with intermitted lag synchronization (ILS) [Phys. Rev. E 62, 7497 (2000)].Synchronization [1,2] of interacting chaotic oscillators is one of the fundamental phenomena of nonlinear dynamics. Recently several types of chaotic synchronization have been observed in coupled nonlinear oscillators. These are phase synchronization (PS) [3][4][5], lag synchronization (LS) [6][7][8], complete synchronization (CS) [9][10][11][12] and generalized synchronization (GS) [13][14][15]. It is important to note that GS may also takes place in the non-oscillatory chaotic systems (see [16] for detail). All synchronization types are interrelated (see for detail [7,13,17]), but the relationship between them is not completely clarified yet. In recent works [18][19][20][21] it has been shown that all these synchronization types may be considered from the common point of view as different manifestations of one universal phenomenon.It has also been found that onsets of phase and lag synchronization types are preceded by intermittent behavior. Close to the threshold parameter value the coupled chaotic systems demonstrate synchronized dynamics most of the time, but there are time intervals during which the synchronized oscillations are interrupted by non-synchronous behavior. These pretransitional intermittencies have been described in [6,22,23] for the case of lag synchronization and in [24][25][26] for phase synchronization, respectively.Due to the existence of unifying framework of coupled chaotic oscillators synchronization one can also expect the intermitted behavior at the threshold of the generalized synchronization appearance. In this work we consider the behavior of coupled chaotic oscillators close to the coupling parameter value corresponding to the onset of generalized synchronization regime. As it will be shown below the generalized synchronization appearance is also preceded by the intermitted behavior in the same way as the phase synchronization and lag c EDP Sciences

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“…To examine this assumption we have considered the dynamics of two unidirectionally coupled Chua's circuits [31,32] with piecewise linear characteristic (see Fig. 4).…”

mentioning

confidence: 99%

Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

Hramov

Короновский

2005

Europhys. Lett.

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“…A simple circuit consisting of a resistor, inductor and diode showed the period doubling route to chaos (Linsay, 1981). Number of circuits such as Matsumoto's, Chua's, Bronson's and mixed mode have been explored (see Murali et al, 1994;Matsumoto et al, 1987;Bitton et al, 1997) and found to exhibit very rich nonlinear behaviours including periodic, quasiperiodic, quasi-periodic and folded-torus, chaotic etc. (see Kiers et al, 2004;Ikezi et al, 1983;Su et al, 1989;Murali et al, 1995).…”

Section: Introductionmentioning

confidence: 99%

“…(see Kiers et al, 2004;Ikezi et al, 1983;Su et al, 1989;Murali et al, 1995). Matsumoto et al (1987) reported a torus breakdown in the three segment piece-wise sub-circuit. A dissipative non-autonomous chaotic circuit was proposed by Murali et al (1994) using a complex simulation, where the Chua's diode was considered as the source for nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

An analogue circuit to study the forced and quadratically damped Duffing oscillator

Singh

Purohit

Sharma

et al. 2017

IJNDC

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“…Квазипериодические колебания весьма распространены в различных областях науки и техники [1][2][3][4][5][6][7][8]. Поэтому проблема синхронизации таких колебаний является важной зада-чей нелинейной теории.…”

Section: Introductionunclassified

“…Известно не так А. П. Кузнецов, Н. В. Станкевич много примеров квазипериодических генераторов, удобных для анализа методами нелиней-ной динамики. Первым примером, вероятно, является одна из модификаций схемы Чуа [8]. Однако она описывается кусочно-линейной характеристикой и осталась малоизученной в контексте проблем синхронизации квазипериодических колебаний.…”

Section: Introductionunclassified

Synchronization of generators of quasiperiodic oscillations

Кузнецов¹,

Stankevich²

2013

Nelin. Dinam.

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Chaos via torus breakdown

Cited by 100 publications

References 15 publications

Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators

An analogue circuit to study the forced and quadratically damped Duffing oscillator

Synchronization of generators of quasiperiodic oscillations

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