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IEEE Transactions on Circuits and Systems

Issue 8 • Date August 1983

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Displaying Results 1 - 12 of 12
  • Editorial

    Publication Year: 1983, Page(s):509 - 511
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    Freely Available from IEEE
  • A survey of degree theory: Basis and development

    Publication Year: 1983, Page(s):607 - 616
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1344 KB)

    In the first part of this survey the author discusses the basic ideas of degree theory and describes some applications of the Brouwer and Leray-Schauder degrees. The second part briefly describes the extension of the theory to cover successively wider classes of mappings. The references to both parts are given at the end of part II: The reader is frequently referred to some of these references for... View full abstract»

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  • A plain man's guide to bifurcations

    Publication Year: 1983, Page(s):512 - 517
    Cited by:  Papers (6)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (824 KB)

    Bifurcation theory, in its broad sense, includes a large body of theory and techniques for understanding nonlinear systems. Its uses range from deep theoretical understanding (and even wild speculation) to practical engineering design. Its broad applicability is because it deals with qualitative changes such as symmetry breaking as in the buckling of a beam, or appearance of new behavioral modes a... View full abstract»

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  • An introduction to the Lorenz equations

    Publication Year: 1983, Page(s):533 - 542
    Cited by:  Papers (9)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1280 KB)

    Theoretical and numerical results for the three-parameter three-dimensional family of ordinary differential equations known as the Lorenz equations are surveyed. Particular emphasis is laid on the importance of homoclinic bifurcations and their relationship to the appearance of chaotic behaviors. View full abstract»

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  • Measuring Volterra kernels

    Publication Year: 1983, Page(s):571 - 577
    Cited by:  Papers (125)  |  Patents (4)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (912 KB)

    Volterra series have been in the engineering literature for some time now, and yet there have been few attempts to measure Volterra kernels. This paper discusses techniques for measuring the Volterra kernels of weakly nonlinear systems. We introduce a new quick method for measuring the second Volterra kernel which is analogous to pseudonoise testing of a linear device. To illustrate the discussion... View full abstract»

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  • Entropy, Lyapunov exponents, and Hausdorff dimension in differentiable dynamical systems

    Publication Year: 1983, Page(s):599 - 607
    Cited by:  Papers (43)  |  Patents (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1048 KB)

    This is an expository article on the interrelations between three concepts in differentiable dynamical systems: Entropy, Lyapunov exponents, and Hausdorff dimension. The paper begins with an introduction to these concepts and includes a discussion of some recent results. View full abstract»

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  • An algebraic approach to nonlinear functional expansions

    Publication Year: 1983, Page(s):554 - 570
    Cited by:  Papers (149)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1696 KB)

    A new theory of functional expansion is presented which makes use of formal power series in several noncommutative variables and of iterated integrals. A simple closed-form expression for the solution of a nonlinear differential equation with forcing terms is derived, which enables us to give the corresponding Volterra kernels with utmost precision. The noncommutative variables give birth to a sym... View full abstract»

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  • A computer-assisted study of forced relaxation oscillations

    Publication Year: 1983, Page(s):518 - 533
    Cited by:  Papers (13)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1664 KB)

    A piece-wise linear version of the forced relaxation oscillator is studied. Computer results are discussed and informal explanations of some properties of the subharmonic solutions are given. The experimental results display a unique interrelationship between the subharmonics in that all subharmonics can be decomposed into a fundamental set containing the odd order, single-loop subharmonics. View full abstract»

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  • Nonlinear lattice and soliton theory

    Publication Year: 1983, Page(s):542 - 554
    Cited by:  Papers (25)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1280 KB)

    Since the notion of stable pulses, known as solitons, plays a central role in the phenomena of wave propagation in nonlinear systems, an exposition of this topic is developed in some detail. It is known that the equations of motion of the one-dimensional lattice of particles with exponential interaction are integrable, namely, they admit exact solutions, and this system is equivalent to an View full abstract»

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  • Elementary catastrophe theory

    Publication Year: 1983, Page(s):578 - 586
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (1152 KB)

    This tutorial paper explains some of the basic mathematical ideas involved in René Thom's Catastrophe Theory, in the simplest and most accessible case: the Elementary Catastrophes. Topics discussed include the classification of local behavior of smooth functions, determinacy (how much of a Taylor series is adequate to capture the function's behavior), unfoldings (what are the possible perturb... View full abstract»

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  • Toolkit for nonlinear dynamics

    Publication Year: 1983, Page(s):586 - 590
    Cited by:  Papers (5)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (728 KB)

    New tools for the study of qualitative properties of systems of nonlinear ordinary differential equations have been developed during the past fifteen years. This is an expository paper introducing the character of some of these developments. Our intent is to help the reader determine whether the available tools are appropriate for uses he has in mind. View full abstract»

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  • Second-order averaging of forced and coupled nonlinear oscillators

    Publication Year: 1983, Page(s):591 - 598
    Cited by:  Papers (3)
    Request permission for commercial reuse | Click to expandAbstract | PDF file iconPDF (976 KB)

    The classical method of averaging is introduced through a sequence of examples. Various qualitative methods such as normally hyperbolic manifolds and energy methods are used to analyze the averaged equations in such a way that the properties are shown to persist for the actual system of differential equations. View full abstract»

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