Oscillation death and revival by coupling with damped harmonic oscillator

Varshney, Vaibhav; Saxena, Garima; Biswal, B.; Prasad, Awadhesh

doi:10.1063/1.4990482

Cited by 8 publications

(2 citation statements)

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“…Apart from oscillation quenching, counter-rotations may also effect the nature of synchronization giving rise to a new type of "mixed synchronization" [17], where one can observe positive and negative correlations simultaneously in different variables of the system. Recent studies have drawn attention to the significance of including sense of directions in the motion and its possible effects on the dynamics [17,[36][37][38][39]. However, further investigation is required to analyze the combined effects of counter-rotations in the systems with symmetry-breaking coupling, especially when other factors are also considered such as time delay or dimensionality.…”

Section: Discussionmentioning

confidence: 99%

Dynamical effects of breaking rotational symmetry in counter-rotating Stuart-Landau oscillators

et al. 2018

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Stuart-Landau oscillators can be coupled so as to either preserve or destroy the rotational symmetry that the uncoupled system possesses. We examine some of the simplest cases of such couplings for a system of two nonidentical oscillators. When the coupling breaks the rotational invariance, there is a qualitative difference between oscillators wherein the phase velocity has the same sign (termed co-rotation) or opposite signs (termed counter-rotation). In the regime of oscillation death the relative sense of the phase rotations plays a major role. In particular, when rotational invariance is broken, counter-rotation or phase velocities of opposite signs appear to destabilize existing fixed points, thereby preserving and possibly extending the range of oscillatory behavior. The dynamical "frustration" induced by counter-rotations can thus suppress oscillation quenching when coupling breaks the symmetry.

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Section: Discussionmentioning

confidence: 99%

Dynamical effects of breaking rotational symmetry in counter-rotating Stuart-Landau oscillators

et al. 2018

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“…When the mismatch is considerable-as in a mixture of active and inactive oscillators-the coupling is incapable of driving the entire ensemble into a state of sustained oscillation, and instead one finds that above a specific strength gradually all the oscillators are attracted to the fixed point, namely they become inactivated. There are other more subtle effects such as the role played by the sense of rotation of the oscillator phase [23,24], namely the sign of Ω. Whether the phases of two coupled oscillators have the same sign (termed co-rotation) or opposite signs (counter-rotation) can be important when the coupling breaks rotational symmetry, and the dynamical effects of this distinction can be significant [25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Ageing in mixed populations of Stuart–Landau oscillators: the role of diversity

Sahoo¹,

Varshney²,

Prasad³

et al. 2019

J. Phys. A: Math. Theor.

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The phenomenon of ageing in a population of autonomous oscillators, namely the increase in the number of inactive (or non-oscillatory) units due to coupling interactions is studied in a population of globally coupled Stuart–Landau oscillators. The initial populations are prepared either as a mixture of active and inactive oscillators or as an ensemble of active oscillators with a mixture of distinct frequencies. The ageing transition does not depend on whether the coupling breaks gauge symmetry or not, but is affected by the degree of diversity in the ensemble, namely the existence of different types of subsystems that can cause oscillation quenching when coupled. The scaling exponents depend on the nature of the coupling interaction.

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