Amplitude response of coupled oscillators

Aronson, D. G.; Ermentrout, Bard; Kopell, Nancy

doi:10.1016/0167-2789(90)90007-c

Cited by 554 publications

(532 citation statements)

References 26 publications

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“…The Landau-Stuart limit cycle oscillator system [6,40,41] has been an ideal model for the exploration of several of the scenarios we discuss here. This is a two-dimensional oscillator given by the evolution equatioṅ…”

Section: Scenarios For Amplitude Deathmentioning

confidence: 99%

“…Analysis by Aronson, Ermentrout, and Kopell [6] provided a deeper mathematical understanding of this phenomenon. They considered the following system of two Landau-Stuart oscillators, 6).…”

Section: Mismatched Oscillatorsmentioning

confidence: 99%

“…1(c)) and can be different from the null state, X * i ≡ 0. This heterogeneous case has been termed "oscillation death" [1,4,5] or the BarEli Effect [6]), keeping the term amplitude death for the homogeneous case, when a simple transformation can shift the fixed point to the origin [6,7] (as for example in Fig. 1(b)).…”

Section: Introductionmentioning

confidence: 99%

“…Following the initial work by Bar-Eli [1] AD has been studied quite extensively [6,8,9,10]. Different situations where amplitude death occurs have been described, and it is now known that the phenomenon can be seen when the interacting systems are identical [7,11,12,13], mismatched [1,6], when the coupling is dynamical [14], or nonlinear (nondiffusive) [15].…”

Section: Introductionmentioning

confidence: 99%

“…Different situations where amplitude death occurs have been described, and it is now known that the phenomenon can be seen when the interacting systems are identical [7,11,12,13], mismatched [1,6], when the coupling is dynamical [14], or nonlinear (nondiffusive) [15]. We review these various situations and also discuss the general mechanism for AD in Sec.…”

Section: Introductionmentioning

confidence: 99%

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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: Scenarios For Amplitude Deathmentioning

confidence: 99%

“…Analysis by Aronson, Ermentrout, and Kopell [6] provided a deeper mathematical understanding of this phenomenon. They considered the following system of two Landau-Stuart oscillators, 6).…”

Section: Mismatched Oscillatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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Feedback Control Principles for Phase Synchronization

Белых

Osipov

Kurths

2007

Handbook of Chaos Control

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Parity‐Time Symmetry in Magnetic Materials and Devices

Zhang,

Xin,

Liu

2023

Adv Elect Materials

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Non‐Hermitian Hamiltonians may still possess real eigenvalues in case of the existence of parity‐time (PT) symmetry. Exceptional points (EPs) occur at the phase transition from real to complex eigenvalues due to PT‐symmetry breaking in the parameter space. Magnonic devices use magnons to carry, transport, and process information, which have the advantages of low energy dissipation, wave‐based computing, and nonlinear data processing. The combination of PT‐symmetry and magnonics may lead to novel physics as well as unprecedented functional device applications. Recently, the research of PT‐symmetry in magnetism has developed rapidly. In this review, the theoretical predictions as well as experimental findings of PT‐symmetry in magnetism are summarized. First, a brief introduction to PT symmetry, EPs, and anti‐PT symmetry is presented. Second, the theoretical and experimental progress of magnonic PT symmetry are summarized. Third, the theoretical predictions of higher‐order EPs and anti‐PT symmetry in magnonic systems are given. Finally, the study concludes by discussing the future challenges and research prospects in magnonic PT‐symmetry, and proposals for experimental observations of magnonic higher‐order EPs and anti‐PT symmetry are suggested.

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Amplitude response of coupled oscillators

Cited by 554 publications

References 26 publications

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Feedback Control Principles for Phase Synchronization

Parity‐Time Symmetry in Magnetic Materials and Devices

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