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1. Dynamics of circular oscillator arrays subjected to noise

   https://doi.org/10.1007/s11071-021-07165-w  

   Balachandran, B. ; Breunung, T. ; Acar, G. ; Alofi, A. ; and Yorke, J. ( January 2022 , Nonlinear dynamics)

   Energy localization, which are spatially confined response patterns, have been observed in turbomachinery applications, micro-electromechanical systems, and atomic crystals. While confined energy can reduce a device’s life-span, in sensing and energy harvesting applications, it can be beneficial to steer a system’s response into a localized mode. Building on earlier studies, in this article, the authors extend the research on localization by considering an array of coupled Duffing oscillators arranged in a circle. The system is composed of multiple nonlinear oscillators each connected to two neighboring oscillators via springs. Due to the periodic boundary conditions waves can propagate through the boundaries. These oscillators are hardening in most of the considered cases, and softening in the others. In the studied parameter range, the system is characterized by multi-stable behavior and a localized mode as well as a unison-low-amplitude motion coexist. The possibility that white noise can drive the system response from the localized mode to the low amplitude mode and thus suppresses energy localization is investigated. For different noise levels, the duration needed to stop energy localization as well as the probability to suppress localization within a certain time is numerically studied. In addition, the effects of linear coupling and nonlinear coupling between the oscillators on the strength of localization and the minimum noise addition needed to suppress energy localization are examined in depth. Moreover, modeling of large array dynamics with smaller subsystems is explored and dynamics with non-Gaussian noise is also considered. 

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2. Toward Understanding El Niño Southern-Oscillation’s Spatiotemporal Pattern Diversity

   https://doi.org/10.3389/feart.2022.899139  

   Jin, Fei-Fei ( May 2022 , Frontiers in Earth Science)

   The El Niño Southern Oscillation (ENSO) phenomenon, manifested by the great swings of large-scale sea surface temperature (SST) anomalies over the equatorial central to eastern Pacific oceans, is a major source of interannual global shifts in climate patterns and weather activities. ENSO’s SST anomalies exhibit remarkable spatiotemporal pattern diversity (STPD), with their spatial pattern diversity dominated by Central Pacific (CP) and Eastern Pacific (EP) El Niño events and their temporal diversity marked by different timescales and intermittency in these types of events. By affecting various Earth system components, ENSO and its STPD yield significant environmental, ecological, economic, and societal impacts over the globe. The basic dynamics of ENSO as a canonical oscillator generated by coupled ocean–atmosphere interactions in the tropical Pacific have been largely understood. A minimal simple conceptual model such as the recharge oscillator paradigm provides means for quantifying the linear and nonlinear seasonally modulated growth rate and frequency together with ENSO’s state-dependent noise forcing for understanding ENSO’s amplitude and periodicity, boreal winter-time phase locking, and warm/cold phase asymmetry. However, the dynamical mechanisms explaining the key features of ENSO STPD associated with CP and EP events remain to be better understood. This article provides a summary of the recent active research on the dynamics of ENSO STPD together with discussions on challenges and outlooks for theoretical, diagnostic, and numerical modeling approaches to advance our understanding and modeling of ENSO, its STPD, and their broad impacts. 

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3. Using noise to augment synchronization among oscillators

   https://doi.org/10.1038/s41598-021-83806-9  

   Vaidya, Jaykumar ; Bashar, Mohammad Khairul ; Shukla, Nikhil ( December 2021 , Scientific Reports)

   null (Ed.)

   Abstract Noise is expected to play an important role in the dynamics of analog systems such as coupled oscillators which have recently been explored as a hardware platform for application in computing. In this work, we experimentally investigate the effect of noise on the synchronization of relaxation oscillators and their computational properties. Specifically, in contrast to its typically expected adverse effect, we first demonstrate that a common white noise input induces frequency locking among uncoupled oscillators. Experiments show that the minimum noise voltage required to induce frequency locking increases linearly with the amplitude of the oscillator output whereas it decreases with increasing number of oscillators. Further, our work reveals that in a coupled system of oscillators—relevant to solving computational problems such as graph coloring, the injection of white noise helps reduce the minimum required capacitive coupling strength. With the injection of noise, the coupled system demonstrates frequency locking along with the desired phase-based computational properties at 5 × lower coupling strength than that required when no external noise is introduced. Consequently, this can reduce the footprint of the coupling element and the corresponding area-intensive coupling architecture. Our work shows that noise can be utilized as an effective knob to optimize the implementation of coupled oscillator-based computing platforms. 

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4. Synchronization-based model for turbulent thermoacoustic systems

   https://doi.org/10.1007/s11071-023-08368-z  

   Weng, Yue ; Unni, Vishnu R. ; Sujith, R. I. ; Saha, Abhishek ( March 2023 , Nonlinear Dynamics)

   We present a phenomenological reduced-order model to capture the transition to thermoacoustic instability in turbulent combustors. Based on the synchronization framework, the model considers the acoustic field and the unsteady heat release rate from turbulent reactive flow as two nonlinearly coupled sub-systems. To model combustion noise, we use a pair of nonlinearly coupled second-order ODEs to represent the unsteady heat release rate. This simple configuration, while nonlinearly coupled to another oscillator that represents the independent sub-system of acoustics (pressure oscillations) in the combustor, is able to produce chaos. Previous experimental studies have reported a route from low amplitude chaotic oscillation (i.e., combustion noise) to periodic oscillation through intermittency in turbulent combustors. By varying the coupling strength, the model can replicate the route of transition observed and reflect the coupled dynamics arising from the interplay of unsteady heat release rate and pressure oscillations.

    

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5. Dynamics of a system of two coupled third-order MEMS oscillators

   Rand, R ; Shayak, B ; Bhaskar, A ; Zehnder, A. ( November 2020 , International journal of engineering research and applications)

   In this work we present a systematic review of novel and interesting behaviour we have observed in a simplified model of a MEMS oscillator. The model is third order and nonlinear, and we expressit as a single ODE for a displacement variable. We find that a single oscillator exhibits limitcycles whose amplitude is well approximated by perturbation methods. Two coupled identicaloscillators have in-phase and out-of-phase modes as well as more complicated motions.Bothof the simple modes are stable in some regions of the parameter space while the bifurcationstructure is quite complex in other regions. This structure is symmetric; the symmetry is brokenby the introduction of detuning between the two oscillators. Numerical integration of the fullsystem is used to check all bifurcation computations. Each individual oscillator is based on a MEMS structure which moves within a laser-driven interference pattern. As the structure vibrates, it changes the interference gap, causing the quantity of absorbed light to change, producing a feedback loop between the motion and the absorbed light and resulting in a limit cycle oscillation. A simplified model of this MEMS oscillator, omitting parametric feedback and structural damping, is investigated using Lindstedt's perturbation method. Conditions are derived on the parameters of the model for a limit cycle to exist. The original model of the MEMS oscillator consists of two equations: a second order ODE which describes the physical motion of a microbeam, and a first order ODE which describes the heat conduction due to the laser. Starting with these equations, we derive a single governing ODE which is of third order and which leads to the definition of a linear operator called the MEMS operator. The addition of nonlinear terms in the model is shown to produce limit cycle behavior. The differential equations of motion of the system of two coupled oscillators are numerically integrated for varying values of the coupling parameter. It is shown that the in-phase mode loses stability as the coupling parameter is reduced below a certain value, and is replaced by two new periodic motions which are born in a pitchfork bifurcation. Then as this parameter is further reduced, the form of the bifurcating periodic motions grows more complex, with yet additional bifurcations occurring. This sequence of bifurcations leads to a situation in which the only periodic motion is a stable out-of-phase mode. The complexity of the resulting sequence of bifurcations is illustrated through a series of diagrams based on numerical integration. 

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