Dynamics of a ring of three coupled relaxation oscillators

Bridge, Jacqueline; Mendelowitz, Lee; Rand, Richard H.; Sah, Si Mohamed; Verdugo, A.

doi:10.1016/j.cnsns.2008.05.012

Cited by 11 publications

(5 citation statements)

References 15 publications

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“…The stability of such states is analyzed in the Appendix. This case has already been studied in the context of three coupled sinusoidal limit cycle oscillators by Mendelowitz et al [25] and for relaxation limit cycle oscillators by Bridge et al [6], who found that two rotating waves, clockwise and counter-clockwise rotation, are possible.…”

Section: All-in-phase Statesmentioning

confidence: 79%

Bistable chimera attractors on a triangular network of oscillator populations

Martens

2010

Phys. Rev. E

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We study a triangular network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in neighboring populations than to those in their own population. This triangular network is the simplest discretization of a continuous ring of oscillators. Yet it displays an unexpectedly different behavior: in contrast to the lone stable chimera observed in continuous rings of oscillators, we find that this system exhibits two coexisting stable chimeras. Both chimeras are, as usual, born through a saddle node bifurcation. As the coupling becomes increasingly local in nature they lose stability through a Hopf bifurcation, giving rise to breathing chimeras, which in turn get destroyed through a homoclinic bifurcation. Remarkably, one of the chimeras reemerges by a reversal of this scenario as we further increase the locality of the coupling, until it is annihilated through another saddle node bifurcation.

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Section: All-in-phase Statesmentioning

confidence: 79%

Bistable chimera attractors on a triangular network of oscillator populations

Martens

2010

Phys. Rev. E

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Section: Mode-coupling Mediated Interaction Of Two Relaxation-like Cymentioning

confidence: 99%

“…A particularly interesting aspect of the dynamics of the classical limit-cycle relaxation oscillators is their distinctive ability to form highly interacting oscillator networks. 29,30) These networks have been demonstrated in physical systems, and they are equally considered a canonical model for the interaction of neurons in a network, where the neurons themselves are modeled as relaxation oscillators known as the FitzHugh-Nagumo Oscillator. 31,32) A main reason for this interest in coupled relaxation limit-cycle oscillators is their ability to interact via a "Fast Threshold Modulation" mechanism that makes them able to synchronize much faster than their counterparts, the phase oscillators.…”

Section: Mode-coupling Mediated Interaction Of Two Relaxation-like Cy...mentioning

confidence: 99%

Pulse-width modulated oscillations in a nonlinear resonator under two-tone driving as a means for MEMS sensor readout

Houri

Ohta

Asano

et al. 2019

Jpn. J. Appl. Phys.

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A MEMS Duffing resonator is driven by two adjacent frequency tones into the nonlinear regime. We show that if the two-tone drive is applied at a frequency where a bistable response of the nonlinear oscillator exists, then the system output will be modulated by a relaxation cycle caused by periodically jumping between the two solution-branches of the bistable response. Although the jumps are caused by the beating of the drives, the existence and period of this relaxation or hysteresis cycle is not solely dictated by the beat frequency between the two driving tones, but also by their amplitude and detuning with respect to the device resonance frequency. We equally demonstrate how the period of the cycles can be tuned via added tension in the device and how these oscillations can be used as a means of sensitive pulse-width modulated (PWM) readout of MEMS sensors.Template for JJAP Regular Papers 2

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“…The PLA approximation has been used in previous studies to analyze strong relaxation oscillators, such as the Van der Pol oscillator [12] and the Tyson-Fife model [22]. This has proven to be an effective method for studying relaxation oscillators with different coupling mechanisms including diffusive coupling [12] and delay coupling [23], and in systems with two [12], three [24] and four oscillators [25].…”

Section: Piecewise Linear Approximation a Approximating A Single mentioning

confidence: 99%

Synchronization patterns in geometrically frustrated rings of relaxation oscillators

Goldstein

Giver

Chakraborty

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Coupled nonlinear oscillators can exhibit a wide variety of patterns. We study the Brusselator as a prototypical autocatalytic reaction-diffusion model. Working in the limit of strong nonlinearity provides a clear timescale separation that leads to a canard explosion in a single Brusselator. In this highly nonlinear regime, it is numerically found that rings of coupled Brusselators do not follow the predictions from Turing analysis. We find that the behavior can be explained using a piecewise linear approximation.

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Dynamics of a ring of three coupled relaxation oscillators

Cited by 11 publications

References 15 publications

Bistable chimera attractors on a triangular network of oscillator populations

Bistable chimera attractors on a triangular network of oscillator populations

Pulse-width modulated oscillations in a nonlinear resonator under two-tone driving as a means for MEMS sensor readout

Synchronization patterns in geometrically frustrated rings of relaxation oscillators

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