Synchronization in counter-rotating oscillators

Bhowmick, Sourav K.; Ghosh, Dibakar; Dana, Syamal K.

doi:10.1063/1.3624943

Cited by 25 publications

(42 citation statements)

References 33 publications

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“…In this case, the systems are termed corotating, while when the frequencies differ in sign, they are counter-rotating [47]. This latter situation is one of parameter mismatch, and in recent works [47,48,49], the characteristics of AD in such cases have been discussed; see also Sec. 4.…”

Section: Mismatched Oscillatorsmentioning

confidence: 99%

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

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Section: Mismatched Oscillatorsmentioning

confidence: 99%

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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“…The sense of a direction in the rotation of a trajectory of a dynamical system was first introduced by Tabor [17] which was elaborated further by Prasad [14]. A general rule how to change the direction of rotation in a dynamical system was proposed by the authors [9]. It was reported that, in two identical counterrotating oscillators, different pairs of state variables emerge into a mixed CS and antisynchronization(AS) state when a scalar coupling is introduced [9].…”

Section: Introductionmentioning

confidence: 99%

“…We focus on LS and PS scenario that demands more attention since it is more realistic in the larger coupling regime and has potential applications [3,9]. LS in chaotic systems has potential applications in the transmitting information in unidirectionally coupled oscillators [10].…”

Section: Introductionmentioning

confidence: 99%

“…One pair of state variables show LS while another pair is in ALS. Counter-rotation in oscillators is a physical reality as shown in an electronic experiment [9] when two oscillators are characteristically same [14] but their trajectories rotate in opposite directions, clockwise or anticlockwise, in phase space. Physically co-and counter rotating oscillators exist in coupled spherical pendulums, where energy fluctuations in counter-rotating pendulums are found to be higher than in co-rotating case [15].…”

Section: Introductionmentioning

confidence: 99%

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Mixed lag synchronization in chaotic oscillators and experimental observations

Bera

Bhowmick²,

Ghosh

2015

Int. J. Dynam. Control

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We report mixed lag synchronization in coupled counter-rotating oscillators. The trajectories of counterrotating oscillators has opposite directions of rotation in uncoupled state. Under diffusive coupling via a scalar variable, a mixed lag synchronization emerges when a parameter mismatch is induced in two counter-rotating oscillators. In the state of mixed lag synchronization, one pair of state variables achieve synchronization shifted in time while another pair of state variables are in antisynchronization, however, they are too shifted by the same time. Transition point of mixed-phase synchronization is estimated analytically using approximation theory. Numerical example of the paradigmatic Rössler oscillator is presented and supported by electronic experiment.

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“…Noise induced effects may lead to interesting behavior for coupled oscillators, in particular, oppositely rotating coupled oscillators (see, for example, [20,21]). Our analysis could also be extended to include colored noise as discussed in [7].…”

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confidence: 99%

Effects of Moderate Noise on a Limit Cycle Oscillator: Counterrotation and Bistability

Newby

Schwemmer

2014

Phys. Rev. Lett.

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The effects of noise on the dynamics of nonlinear systems is known to lead to many counterintuitive behaviors. Using simple planar limit cycle oscillators, we show that the addition of moderate noise leads to qualitatively different dynamics. In particular, the system can appear bistable, rotate in the opposite direction of the deterministic limit cycle, or cease oscillating altogether. Utilizing standard techniques from stochastic calculus and recently developed stochastic phase reduction methods, we elucidate the mechanisms underlying the different dynamics and verify our analysis with the use of numerical simulations. Lastly, we show that similar bistable behavior is found when moderate noise is applied to the more biologically realistic FitzHugh-Nagumo model.Limit cycle oscillators have been widely used to model various natural phenomena [1][2][3]. As such, they have been the subject of extensive study in the field of nonlinear science. In recent years, the effects of noise on the dynamics of limit cycle oscillators has received much interest [4][5][6][7][8]. When the noise is weak, formal reduction methods can be performed to reduce the dimensionality of the system to a so-called phase equation [7,8]. In this case, one can analytically show that both the magnitude (and correlation time for colored noise) of the added noise shift the mean frequency of oscillations away from the natural frequency of the limit cycle. On the other hand, when the noise is large, the trajectories of the system appear completely random and bear no resemblance to the deterministic limit cycle behavior.The case of moderate noise applied to a limit cycle oscillator has received less attention. It is known that moderate noise can cause stochastic resonance in systems close to a bifurcation to limit cycle oscillations [9,10], and in systems where limit cycles arise as the result of periodic forcing [4]. However, an exploration of how moderate noise interacts with the underlying deterministic dynamics of a system displaying limit cycle behavior has not yet been undertaken and is the purpose of the current Letter. We find that an oscillator subject to moderate noise can display numerous interesting and counterintuitive behaviors. In some cases, the addition of noise causes the phase to behave like a bistable switch, while in other cases noise can act to completely eliminate oscillations, and even cause the trajectories to rotate in the opposite direction of the deterministic limit cycle.Bistability in the amplitude of the limit cycle has been shown to occur in the Stuart-Landau (SL) system when it is subjected to periodic forcing [11], or specially constructed stochastic forcing [12]. It is also known that coupling limit cycle oscillators together can eliminate oscillations [13,14]. However, we show that these phenomena can occur in a planar limit cycle system when each component is subjected to additive white noise.For simplicity, we consider a radially symmetric deterministic system. One such symmetric oscillator that we employ is the ...

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Synchronization in counter-rotating oscillators

Cited by 25 publications

References 33 publications

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Mixed lag synchronization in chaotic oscillators and experimental observations

Effects of Moderate Noise on a Limit Cycle Oscillator: Counterrotation and Bistability

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