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Application of the describing function to the Danziger-Elmegreen equations

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Abstract

The describing function method is used as a guide to the behaviour of the solutions of the equations of Danziger and Elmergreen, proposed as a model of periodic catatonia. The method suggests that whenever the equilibrium point is unstable it is surrounded by a stable closed periodic orbit. This is confirmed in specific cases by computation.

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Literature

  • Cronin, J. 1973. “The Danziger-Elmergreen theory of periodic catatonic schizophrenia”.Bull. Math. Biol.,35, 689–708.

    MATH  MathSciNet  Google Scholar 

  • — 1974. “A mathematical model for catatonic schizophrenia.”Ann. N.Y. Acad. Sci.,31, 112–122.

    Google Scholar 

  • Danziger, L. and G. L. Elmergreen. 1954. “Mathematical theory of periodic relapsing catatonia.”Bull. Math. Biophys.,16, 15–21.

    Google Scholar 

  • — and —. 1958. “Mechanism of Periodic Catatonia.”Confin. Neurol.,18, 159–166.

    Google Scholar 

  • Di Stefano, J. J. 1969. “A Model of the regulation of circulating thyroxin”.Math. Biosci.,4, 137–152.

    Article  Google Scholar 

  • Friedrichs K. O. 1965.Advanced Ordinary Differential Equations. New York: Gordon and Breach.

    Google Scholar 

  • Gjessing, R. 1939. “Beitrage zur Kenntnis der Pathophysiologie periodisch katatoner Zustande”.Archs Psychiat.,109, 525–595.

    Article  Google Scholar 

  • Rapp, P. E. 1975a. “Biochemical oscillators: a search procedure.”Math. Biosci.,23, 289–304.

    Article  MATH  MathSciNet  Google Scholar 

  • — 1975b. “A theoretical investigation of a large class of biochemical oscillators.”Math. Biosci.,25, 165–188.

    Article  MATH  MathSciNet  Google Scholar 

  • Rashevsky, N. 1968. “Mathematical theory of biological periodicities: formulation of then-body case.”Bull. Math. Biophys.,30, 735–749.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Natural Philosophy, The University, G12 8QQ, Glasgow, U.K.

    N. MacDonald

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  1. N. MacDonald
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MacDonald, N. Application of the describing function to the Danziger-Elmegreen equations. Bltn Mathcal Biology 38, 453–458 (1976). https://doi.org/10.1007/BF02462219

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  • DOI: https://doi.org/10.1007/BF02462219

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