Abstract
Properties of the solutions of the mathematical model introduced by Danziger and Elmergreen for the study of periodic catatonic schizophrenia are studied, and it is shown that the properties established suggest that the model can be used to study other forms of catatonic schizophrenia besides periodic catatonic schizophrenia.
Similar content being viewed by others
Literature
Andronow, A. A. and C. E. Chaikin. 1949.Theory of Oscillations, English Language Edition, Lefschetz, S., ed. Princeton: Princeton University Press.
Cesari, L. 1959.Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, 2nd ed. Berlin: Springer-Verlag.
Coddington, E. A. and N. Levinson. 1955.Theory of Ordinary Differential Equations. New York: McGraw-Hill.
Cronin, J. 1967. “Recurrent Solutions of Some Autonomous Equations.”J. Diff. Eqns,3, 595–600.
Danziger, L. 1958. “Thyroid Therapy of Schizophrenia.”Dis. Nervous System,19, 2–7.
— and G. L. Elmergreen. 1954. “Mathematical Theory of Periodic Relapsing Catatonia.”Bull. Math. Biophysics,16, 15–21.
— and —. 1954. “The Thyroid-Pituitary Homeostatic Mechanisms.” —Ibid.,18, 1–13.
— and —. 1957. “Mathematical Models of Endocrine Systems.” —Ibid.,19, 9–18.
— and —. 1958. “Mechanism of Periodic Catatonia.”Confinia Neurologica,18, 159–166.
— and J. A. Kindwall. 1953. “Thyroid Therapy in Some Mental Disorders.”Dis. Nervous System,14, 3–13.
Danziger, L. and J. A. Kindwall. “Treatment of Periodic Relapsing Catatonia.”Ibid., Dis. Nervous System,15, 35–43.
Freedman, A. M., H. I. Kaplan and H. S. Kaplan (eds.). 1967.Comprehensive Textbook of Psychiatry. Baltimore: Williams & Wilkins.
Gjessing, R. 1932. “Beitrage zur Kenntnis der Pathophysiologie des Katatonen Stupors.”Arch. Psychiat.,96, 319–393.
— 1935. “Beitrage zur Kenntnis der Pathophysiologie der Katatonen Erregung.” —Ibid.,,104, 355–416.
— 1938. “Disturbances of Somatic Function in Catatonia With a Periodic Course and Their Compensation.”J. Ment. Sci.,84, 608–621.
— 1939. “Beitrage zur Kenntnis der Pathophysiologie Periodisch Katoner Zustande.”Arch. Psychiat.,109, 525–595.
—. “Beitrage zur Somatologie der Periodischen Katatonie.”—Ibid.,121, 191–326.
Lefschetz, S. 1961. “The Critical Case in Differential Equations.”Bol. Soc. Mat. Mex.,1, 5–18.
— 1962.Differential Equations: Geometric Theory, 2nd ed. New York: Interscience.
Marden, M. 1949.The Geometry of the Zeros of a Polynomial in a Complex Variable, Mathematical Surveys, No. III, Providence: American Mathematical Society.
Minorsky, N. 1962.Nonlinear Oscillations. Princeton: Van Nostrand.
Nemytskii, V. V. and V. V. Stepanov. 1960.Qualitative Theory of Differential Equations. Princeton: Princeton University Press.
Rashevsky, N.Some Medical Aspects of Mathematical Biology. Springfield: C. C. Thomas.
Richter, C. P. 1965.Biological Clocks in Medicine and Psychiatry Springfield: C. C. Thomas.
Riggs, D. S. 1970.Control Theory and Physiological Feedback Mechanisms. Baltimore: Williams & Wilkins.
Zubov, V. I. 1957.Methods of A. M. Lyapunov and Their Application (in Russian). (Translated by the United States Atomic Energy Commission, AEC-tr-4439). Moscow.
Author information
Authors and Affiliations
Additional information
The research in this paper was supported by the U.S. Army Research Office (Durham) (Grant No. DA-ARO-D-31-124-G1098) and by a Rutgers Research Council Faculty Fellowship.
Rights and permissions
About this article
Cite this article
Cronin, J. The Danziger-Elmergreen theory of periodic catatonic schizophrenia. Bltn Mathcal Biology 35, 689–707 (1973). https://doi.org/10.1007/BF02458370
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02458370