Researcher:
Şuvak, Önder

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PhD Student

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Önder

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Şuvak

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Şuvak, Önder

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2009 - 200912010 - 20112

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    Computing quadratic approximations for the isochrons of oscillators: a general theory and advanced numerical methods
    (IEEE-Inst Electrical Electronics Engineers Inc, 2009) Department of Electrical and Electronics Engineering; N/A; Demir, Alper; Şuvak, Önder; Faculty Member; PhD Student; Department of Electrical and Electronics Engineering; College of Engineering; Graduate School of Sciences and Engineering; 3756; N/A
    We first review the notion of isochrons for oscillators, which has been developed and heavily utilized in mathematical biology in studying biological oscillations. Isochrons were instrumental in introducing a notion of generalized phase for an oscillation and form the basis for oscillator perturbation analysis formulations. Calculating the isochrons of an oscillator is a very difficult task. Except for some very simple planar oscillators, isochrons can not be calculated analytically and one has to resort to numerical techniques. Previously proposed numerical methods for computing isochrons can be regarded as brute-force, which become totally impractical for non-planar oscillators with dimension more than two. In this paper, we present a precise and carefully developed theory and advanced numerical techniques for computing local but quadratic approximations for isochrons. Previous work offers the theory and the numerical methods needed for computing only linear approximations for isochrons. Our treatment is general and applicable to oscillators with large dimension. We present examples for isochron computations, verify our results against exact calculations in a simple case, and allude to several applications among many where quadratic approximations of isochrons will be of use. Copyright 2009 ACM.
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    Quadratic approximations for the isochrons of oscillators: a general theory, advanced numerical methods, and accurate phase computations
    (IEEE-Inst Electrical Electronics Engineers Inc, 2010) N/A; Department of Electrical and Electronics Engineering; Şuvak, Önder; Demir, Alper; PhD Student; Faculty Member; Department of Electrical and Electronics Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 3756
    The notion of isochrons for oscillators, introduced by Winfree and thereon heavily utilized in mathematical biology, were instrumental in introducing a notion of generalized phase and form the basis for oscillator perturbation analyses. Computing isochrons is a hard problem, existing brute-force methods incurring exponential complexity. In this paper, we present a precise and carefully developed theory and numerical techniques for computing local but quadratic approximations for isochrons. Previous work offers the techniques needed for computing only local linear approximations. Our treatment is general and applicable to oscillators with large dimension. We present examples for isochron computations, verify our results against exact calculations in a simple analytically calculable case, test our methods on complex oscillators, and show how quadratic approximations of isochrons can be used in formulating accurate, novel phase computation schemes and finally allude to second-order accurate compact phase macromodels. Oscillator studies seem to have progressed independently in electronics and biology. Even though analyses in electronics did not make use of the notion of isochrons, similar models and methods, expressed in totally different terminologies, have been developed in both disciplines. In this paper, we also reveal the connection between oscillator analysis work in these two seemingly disparate disciplines.
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    On phase models for oscillators
    (IEEE-Inst Electrical Electronics Engineers Inc, 2011) N/A; Department of Electrical and Electronics Engineering; Şuvak, Önder; Demir, Alper; PhD Student; Faculty Member; Department of Electrical and Electronics Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 3756
    Oscillators have been a research focus for decades in many disciplines such as electronics and biology. The time keeping capability of oscillators is best described by the scalar quantity phase. Phase computations and equations describing phase dynamics have been useful in understanding oscillator behavior and designing oscillators least affected by disturbances such as noise. In this paper, we present a unified theory of phase equations assimilating the work that has been done in electronics and biology for the last seven decades. We first provide a review of isochrons, which forms the basis of a generalized phase notion for oscillators. We present a general framework for phase equations and derive an exact phase equation that is practically unusable but facilitates the derivation of usable ones based on linear (already known) and quadratic (new and more accurate) approximations for isochrons. We discuss the utility of these phase equations in performing (semi) analytical phase computations and also describe simpler and more accurate phase computation schemes. Numerical experiments on several examples are presented comparing the accuracy of the various phase equations and computation schemes described in this paper.