Nonlinear phenomena emerging from the coupled behaviour of a pair of oscillators have attracted considerable research attention over the years, of which, amplitude death (AD) and phase-flip bifurcation (PFB) are two noteworthy examples. Although theoretical research has postulated the coexistence of AD and PFB upon variation of different control parameters, such an occurrence has not been reported in practical systems. Here, we provide the first experimental evidence of the coexistence of AD and PFB in a physical system, comprising of a coupled pair of candle-flame oscillators. As the strength of coupling between the oscillators is increased, we report a decrease in the span of AD region between the states of in-phase and anti-phase oscillations, leading up to a point of PFB. Understanding such a switching of phenomena between AD and PFB helps us to evade their undesirable occurrences such as AD in neuron and brain cells, oscillatory state in prey-predator systems, oscillatory spread of epidemics and so forth. © 2018, The Author(s).

R. I. Sujith

Department of Aerospace Engineering

Krishna Manoj

Samadhan A. Pawar

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Scientific Reports

Oscillatory instabilities, although ubiquitous in nature, are undesirable in many situations such as biological systems, swaying of bridges and skyscrapers, aero-acoustic flutter, prey-predator and disease spread models, and thermoacoustic systems, where they exhibit large amplitude periodic oscillations. In the present study, we aim to study the suppression mechanism of such undesired oscillations in a pair of thermoacoustic oscillators, also known as horizontal Rijke tubes. These oscillators are coupled through a connecting tube whose length and diameter are varied as coupling parameters. With the variation of these parameters, we show the first experimental evidence of rich dynamical phenomena such as synchronization, amplitude death, and phase-flip bifurcation in coupled identical thermoacoustic oscillators. We discover that when frequency and amplitude mismatch are introduced between these oscillators, quenching of oscillations in one or both the oscillators occurs with further ease, through the mechanisms of amplitude death and partial amplitude death. Finally, we show that the effectiveness of coupling is sensitive to the dimensions of the connecting tube which can be directly correlated with the time delay and coupling strength of the system. © 2019 Author(s).

Chaos

Oscillation quenching and phase-flip bifurcation in coupled thermoacoustic systems

We investigate the coupled behaviour of two oscillatory flames produced by separate bundles of candles, referred to as candle-flame oscillators, as the distance between them is varied. Each bundle consists of four candles whose individual flames are fused so that the resultant flame produces self-sustained limit cycle oscillations. The recent study by Manoj et al. [Scientific Reports 8, 11626 (2018)] has reported the occurrence of four different modes of coupled behaviour, which include in-phase synchronization, amplitude death, anti-phase synchronization, and desynchronization by observing the flame dynamics of such coupled candle-flame oscillators. Here, we investigate the physical mechanism behind the occurrence of these different dynamical modes. Towards this purpose, we perform simultaneous measurements of the flow field around the candle flames using high-speed shadowgraph and of the reaction zone of each flame using high-speed CH ∗ chemiluminescence imaging. We notice that these modes are distinguished by the distinct features of the flame dynamics and the corresponding buoyancy-induced flows surrounding the flames. We observe that the difference in the interaction of vortices, formed due to the instability of buoyancy-induced flows around each flame at various distances, plays a significant role in inducing different modes of coupled dynamics between the oscillators. Furthermore, we find that the change in the length scales of vortices shed around the flames is a contributing factor in increasing the frequency of the oscillators during the transition from in-phase to anti-phase mode of synchronization. © 2019 Author(s).

AIP Advances

Role of buoyancy-driven vortices in inducing different modes of coupled behaviour in candle-flame oscillators

Synchronization and chimera are examples of collective behavior observed in an ensemble of coupled nonlinear oscillators. Recent studies have focused on their discovery in systems with least possible number of oscillators. Here we present an experimental study revealing the synchronization route to weak chimera via quenching, clustering, and chimera states in a single system of four coupled candle-flame oscillators. We further report the discovery of multiphase weak chimera along with experimental evidence of the theoretically predicted states of in-phase chimera and antiphase chimera. © 2019 American Physical Society.

Physical Review E

Synchronization route to weak chimera in four candle-flame oscillators

Experimental Evidence of Amplitude Death and Phase-Flip Bifurcation between In-Phase and Anti-Phase Synchronization

Coupling nonlinear dynamical systems can lead to a host of phenomena, one of which leads to the complete cessation of their oscillations. This phenomenon is referred to as amplitude death (AD) in the dynamical systems literature. Recently, there is a growing interest to mitigate oscillatory or dynamic instabilities in a variety of engineering systems using AD. Deriving impetus from the same, we investigate the possibility of cessation of oscillatory instabilities in aeroelastic systems using the concept of AD. In specific, the suppression of flutter instability that arises in aeroelastic systems due to highly nonlinear fluid–structure interactions is investigated from the purview of AD. To that end, we consider two identical airfoils that are exposed to input fluid forces along the axial directions. The airfoils, via translational and rotational springs, are allowed to oscillate in plunge and pitch degrees of freedom. To augment the findings to in-field scenarios, we consider the individual cases of the input flow to be either uniform (deterministic) or possess randomly time varying components, respectively. To promote coupled interactions, the airfoils are coupled using a linear torsional spring. The coupled interaction of the airfoils at the flutter regime are then studied by obtaining the pitch and plunge responses. Further, the strength of the coupling and the time delay between the airfoils are systematically varied to investigate its effect on the regime of AD. The ability of AD to suppress flutter instability and thereby serve as a possible flutter suppression mechanism in both deterministic and stochastic input flow cases is then demonstrated. Finally, the phase delay values between the airfoils is computed to heuristically present a relationship between the coupling parameters and the post coupling signatures. © 2020 Elsevier Ltd

Journal	Scientific Reports
Publisher	Nature Publishing Group
ISSN	20452322
Open Access	No