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IEEE Transactions on Circuits and Systems

Issue 9 • September 1983

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Displaying Results 1 - 12 of 12
  • Editorial in special issue

    Publication Year: 1983, Page(s):617 - 619
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    Freely Available from IEEE
  • Effect of a periodic perturbation on radio frequency model of Josephson junction

    Publication Year: 1983, Page(s):633 - 636
    Cited by:  Papers (37)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (472 KB)

    By using the analytical method of Mel'nikov the qualitative behavior of the single differential equation \ddot{x}+\delta dot{x}- \alpha \sin x = f_{0} + f_{1} \sin(\omega t), dot{x}stackrel{\Delta }{=} frac{dx}{dt} where \delta > 0, \alpha > 0, f_{0} \geq 0, f_{1} > 0, \omega > 0 is studied. The parameter space View full abstract»

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  • Uniqueness of a basic nonlinear structure

    Publication Year: 1983, Page(s):648 - 651
    Cited by:  Papers (22)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (488 KB)

    In this paper we show that systems consisting of a memoryless nonlinearity sandwiched between two linear time-invariant (LTI) operators are unique modulo scaling and delays. We mention a few corollaries and applications of general circuit and system theoretic interest. View full abstract»

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  • Complicated, but rational, phase-locking responses of an ideal time-base oscillator

    Publication Year: 1983, Page(s):627 - 632
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (752 KB)

    A model is advanced to account for the complicated phase-locking responses of a prototypical time-base oscillator driven by a train of excitory pulses. The model predicts that the intervals of stability for different ratios of phase locking should occur in specific sequences as functions of the parameters. With respect to variation of one parameter (a strength of coupling), these sequences compris... View full abstract»

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  • A generalized Fock space framework for nonlinear system and signal analysis

    Publication Year: 1983, Page(s):637 - 647
    Cited by:  Papers (71)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1280 KB)

    A unified framework is presented for nonlinear (and, in particular, linear) system and signal analysis, whereby a number of problems involving approximation and inversion of nonlinear functions, nonlinear functionals, and nonlinear operators, are cast in a reproducing kernel Hilbert space (RKHS) setting, and solved by orthogonal projection methods. The RKHS's used for the above purpose are the "ar... View full abstract»

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  • Nonelementary catastrophe theory

    Publication Year: 1983, Page(s):663 - 670
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1024 KB)

    This tutorial paper is intended to complement the preceding one on Elementary Catastrophe Theory, and to emphasize that many of the supposed limitations of the elementary catastrophes may be overcome by suitably modifying the mathematical setting. The main generalization discussed here is the Imperfect Bifurcation Theory of Golubitsky and Schaeffer Catastrophe Theory with a distinguished parameter... View full abstract»

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  • A criterion of existence and uniqueness of the stable limit cycle in second-order oscillators

    Publication Year: 1983, Page(s):680 - 683
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (432 KB)

    Conditions that ensure the existence of a single stable limit cycle in second-order oscillators are found. These conditions enable to characterize both the required nonlinear element and the range of values of the linear circuit parameters in a simple way. It will be shown how these conditions can be applied to the design of the commonly used oscillators. View full abstract»

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  • Synchronization and chaos

    Publication Year: 1983, Page(s):620 - 626
    Cited by:  Papers (74)  |  Patents (2)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (832 KB)

    We believe that synchronization and chaos are closely related. Common intuition suggests that when a circuit is off synchronization the observed output, although not periodic, will be a sum of periodic (intermodulation) components. In fact, at least for a large class of systems we have studied, the output does not have this relatively simple form but is actually chaotic. This paper studies a simpl... View full abstract»

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  • Chaos and Arnold diffusion in dynamical systems

    Publication Year: 1983, Page(s):697 - 708
    Cited by:  Papers (14)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1488 KB)

    Chaotic motion refers to complicated trajectories in dynamical systems. It occurs even in deterministic systems governed by simple differential equations and its presence has been experimentally verified for many systems in several disciplines. A technique due to Melnikov provides an analytical tool for measuring chaos caused by horseshoes in certain systems. The phenomenon of Arnold diffusion is ... View full abstract»

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  • The effects of small noise on implicitly defined nonlinear dynamical systems

    Publication Year: 1983, Page(s):651 - 663
    Cited by:  Papers (11)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1536 KB)

    The dynamics of a large class of nonlinear systems are described implicitly, i.e., as a combination of algebraic and differential equations. These dynamics admit of jump behavior. We extend the deterministic theory to a stochastic theory since (i) the deterministic theory is restrictive, (ii) the macroscopic deterministic description of dynamics frequently arises from an aggregation of microscopic... View full abstract»

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  • On stability preserving mappings

    Publication Year: 1983, Page(s):671 - 679
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1080 KB)

    We view systems as mappings which connect a set of inputs (input functions) with a set of outputs (output functions). Such systems are said to be stability preserving if a stable (asymptotically stable) reference input results in an output with the same stability properties. In the present paper we study the properties of such mappings, we establish a block diagram algebra for such mappings, and w... View full abstract»

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  • On the stability of limit cycles in nonlinear feedback systems: Analysis using describing functions

    Publication Year: 1983, Page(s):684 - 696
    Cited by:  Papers (17)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1320 KB)

    In this paper we establish computable conditions for the stability and instability of limit cycles in nonlinear feedback systems. In the proof of the present results, we make use of several novel transformations, of averaging, and of a result on integral manifolds and we assume that we can establish the existence of limit cycles by means of the describing function method. Our results, which in par... View full abstract»

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