Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators

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dc.contributor.author Lal, Nijil
dc.contributor.author Parmananda, Punit
dc.contributor.author Das Gupta, Kantimay
dc.contributor.author Chakrabarty, Nilaj
dc.contributor.author Jain, Aditya
dc.date.accessioned 2017-01-31T06:08:56Z
dc.date.available 2017-01-31T06:08:56Z
dc.date.issued 2017-01
dc.identifier.citation Chakrabarty, Nilaj; Jain, Aditya; Lal, Nijil; Das Gupta, Kantimay and Parmananda, Punit, “Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators”, Chaos: An Interdisciplinary Journal of Nonlinear Science, DOI: 10.1063/1.4974071, vol. 27, no. 1, Jan. 2017. en_US
dc.identifier.issn 1054-1500
dc.identifier.issn 1089-7682
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/2649
dc.identifier.uri http://dx.doi.org/10.1063/1.4974071
dc.description.abstract In this paper, we present an experimental setup and an associated mathematical model to study the synchronization of two self-sustained, strongly coupled, mechanical oscillators (metronomes). The effects of a small detuning in the internal parameters, namely, damping and frequency, have been studied. Our experimental system is a pair of spring wound mechanical metronomes; coupled by placing them on a common base, free to move along a horizontal direction. We designed a photodiode array based non-contact, non-magnetic position detection system driven by a microcontroller to record the instantaneous angular displacement of each oscillator and the small linear displacement of the base, coupling the two. In our system, the mass of the oscillating pendula forms a significant fraction of the total mass of the system, leading to strong coupling of the oscillators. We modified the internal mechanism of the spring-wound “clockwork” slightly, such that the natural frequency and the internal damping could be independently tuned. Stable synchronized and anti-synchronized states were observed as the difference in the parameters was varied in the experiments. The simulation results showed a rapid increase in the phase difference between the two oscillators beyond a certain threshold of parameter mismatch. Our simple model of the escapement mechanism did not reproduce a complete 180° out of phase state. However, the numerical simulations show that increased mismatch in parameters leads to a synchronized state with a large phase difference. We provide experimental and numerical evidence of phase locked synchronous states in a system of two strongly coupled mechanical oscillators. By designing an opto-electronic position tracking system using linear photosensor arrays, we track the motion of individual oscillators. Our mathematical model allows for independently detuning key metronome parameters like frequency and damping coefficient. We present two important results: (A) experimental evidence that two strongly coupled metronomes can be made to synchronize in states of in-phase and anti-phase synchrony by changing their relative parameter mismatch, and (B) numerical evidence of rapidly increasing phase difference of the two oscillators beyond a certain threshold of parameter mismatch. Our results demonstrate that increased mismatch of parameters can be a possible underlying reason behind out of phase synchronization. I. INTRODUCTION en_US
dc.description.statementofresponsibility by Nilaj Chakrabarty, Aditya Jain, Nijil Lal, Kantimay Das Gupta, and Punit Parmananda
dc.format.extent Vol. 27, no. 1
dc.language.iso en_US en_US
dc.publisher AIP Publishing en_US
dc.subject Photodetectors en_US
dc.subject Clocks en_US
dc.subject Coupled oscillators en_US
dc.subject Tracking devices en_US
dc.subject Acoustic modeling en_US
dc.title Effect of parameter mismatch on the dynamics of strongly coupled self sustained oscillators en_US
dc.type Article en_US

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