Nonlinear Dynamical Patterns as Personality Theory for Neurobiology and Psychiatry

Psychiatry (New York)

Volumn 58, Issue 4, 1995, Pages 371-390

  Mandell, Arnold J ^a   Selz, Karen A ^a  

^a FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ARTIFICIAL NEURAL NETWORK; BEHAVIOR; CHARACTER; CLASSIFICATION; FORECASTING; HUMAN; MENTAL DISEASE; NEUROBIOLOGY; PATHOPHYSIOLOGY; PERSONALITY; PHYSIOLOGY; PSYCHIATRY; PSYCHOANALYTIC THEORY; PSYCHOLOGICAL ASPECT; SYSTEMS THEORY;

BEHAVIOR; CHARACTER; FORECASTING; HUMANS; MENTAL DISORDERS; NEURAL NETWORKS (COMPUTER); NEUROBIOLOGY; PERSONALITY; PSYCHIATRY; PSYCHOANALYTIC THEORY; SYSTEMS THEORY;

EID: 0029400066     PISSN: 00332747     EISSN: 1943281X     Source Type: Journal    
DOI: 10.1521/00332747.1995.11024741     Document Type: Article

References (76)

1. American Psychiatric Association. Diagnostic and Statistical Manual of Mental Disorders (3rd ed., rev). APA, 1987.
2. Arnold, V. I. Geometric Methods in the Theory of Ordinary Differential Equations. Springer, 1983.
3. Batchelor, G. K. The Theory of Homogenous Turbulence. Cambridge University Press, 1953.
4. Bleuler, E. Dementia Praecox. International Universities Press, 1911.
5. Bowen, R., and Ruelle, D. The ergodic theorem for Axiom A flows. Invent. Math. (1975) 29:181-202.
6. Cartwright, M. L., and Littlewood, J. E. On nonlinear equations of the second order. Journal of the London Mathematical Society (1945) 20:180-89.
7. Collet, P., and Eckmann, J -P. Iterated Maps on the Interval as Dynamical Systems. Basel: Birkhausen 1980.
8. Devaney, R. L. An Introduction to Chaotic Dynamical Systems. Menlo Park: Benjamin-Cummings, 1985.
9. Eckmann, J. P., and Ruelle, D. Ergodic theory of chaos and strange attractors. Reviews of Modern Physics (1985) 57:617-56.
10. Ehlers, C, Russo, P. V., Mandell, A. J., and Bloom, F. E. Architecture of rat nocturnal locomotion: A predictive descriptor of the effects of antidepressant and antimanic treatments. Psycho-pharmacology Bulletin (1983) 19:692-5.
11. Feigenbaum, M. J. Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics (1978) 19:25-52.
12. Fenichel, O. Psychoanalysis of character. In H. Fenichel and D.Rappaport, eds., The Collected Papers of Otto Fenichel. Norton, 1954, pp 198-214.
13. Fermi, E. Thermodynamics. Prentice Hall, 1937.
14. Geschwind, N. Interiectal behavioral changes in epilepsy. Epilepsia (1983) 24:523-30.
15. Guckenheimer, J., and Holmes, P. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, 1983.
16. Hartmann, H., Kris, E., and Lowenstein, R. M. Comments on the formation of psychic structure. The Psychoanalytic Study of the Child (1946) 2: 11-38.
17. Horowitz, M. J. Introduction to Pschyodynamics: A New Synthesis. Basic Books, 1988.
18. James, W. The Writings of William James Chicago: Chicago University Press, 1977.
19. Jaspers, K. General Psychopathology. Manchester: Manchester University Press, 1959.
20. Joseph, D. D. Stability of Fluid Motions, I and II. New York: Springer, 1976.
21. Kernberg, O. Borderline Conditions and Pathological Narcissism. New York: Jason Aronson, 1975.
22. Knapp, S., Ehlers, C. L., Russo, P. V., and Mandell, A. J. A cross-disciplinary approach to the action of lithium: A vertical intergration. In: Lux, H., Aldenhott, J. Emrich, H. eds. Basic Mechanisms in the Action of Lithium. New York: Excerpta Medica, 1981a. pp 102-120.
23. Knapp, S., and Mandell, A. J. TRH influences the pterin cofactor-and time-dependent instabilities of rat raphe tryptophan hydroxylase activity assessed under far-from-equilibrium conditions. Neurochem Internat. (1984) 6:801-12.
24. Knapp, S., and Mandell, A. J. Lithium and chlorimipramine differentially alter the stability properties of tryptophan hydroxylase as seen in allosteric and scattering kinetics. J. Psychiatric. Res. (1983) 28:19-24.
25. Knapp, S., Mandell, A. J., Russo, P. V., Vitto, A., and Stewart, K. Strain differences in kinetic and thermal stability of two mouse brain tryptophan hydroxylase activities. Brain Research (1981b) 230:317-336.
26. Kolmogorov, A. N. General theory of dynamical systems and classical mechanics. Proceedings of the 1954 International Congress of Mathematics. North-Holland, 1957, pp.315-33.
27. Langs, R., Rapp, P. E., Pinto, A., Cramer, G. and Badalamenti, A. Three quantitative studies of gender and identity in psychotherapy consultations. American Journal of Psychotherapy (1992) 46:183-206.
28. Mandell, A. J. Nonlinear dynamics in brain processes. Psychopharmacology Bulletin (1982) 18-63.
29. Mandell, A. J. From intermittency to transitivity in neuropsychobiological flows. American Journal of Physiology (1983) 245(14):R484-R494.
30. Mandell, A. J. Non-equilibrium behavior of some brain enzyme and receptor systems. Annual Review of Pharmacology and Toxicology (1984) 24: 237-74.
31. Mandell, A. J. Toward a neuropharmacology of habituation: A vertical integration. Mathematical Modeling (1986) 7:809-88.
32. Mandell, A. J. Dynamical complexity and pathological order in the cardiac monitoring problem. Physica (1987) 27D:235-42.
33. Mandell, A. J., Knapp, S., Ehlers, C. L., and Russo, P. V. The stability of constrained randomness: Lithium prophylaxis at several meurobiological levels. In R.J. Post and J.C. Ballenger, eds., The Neurobiology of the Mood Disorders. Williams and Wilkins, 1983, pp. 744-76.
34. Mandell, A. J., and Russo, P. V. Striatal tyrosine hydroxylase activity: Multiple conformational kinetic oscillators and product concentration frequencies. Journal of Neuroscience (1981) 1:380-9.
35. Mandell, A. J., Russo, P. V., and Knapp, S. Strange stability in hierarchically coupled neuropsychobiological systems. In: H. Haken, ed, Evolution of Chaos and Order in Physics, Chemistry, and Biology. Springer-Verlag, 1982, pp. 70-286.
36. Mandell, A. J., and Selz, K. A. The new statistical dynamics: An informal look at invariant measures of psychological time series. In R.R. Vallacher and A.J. Novak, eds. Dynamical Systems in Social Psychology. Academic Press, 1994.
37. Mandell, A. J., Selz, K. A., and Schlesinger, M. F. Some comments on the weaving of contemporaneous minds: Resonant neuronal quasiperiodicity, period adding, and O(2) symmetry in the EEG. In D. Duke and W. Prichard, eds., Chaos in the Brain. Singapore: World Scientific Press, 1991, pp. 137-155.
38. Mandell, A. J., Stewart, K. D., and Russo, P. V. The Sunday syndrome: From kinetics to altered consciousness. Federation Proceedings (1981) 40: 2693-8.
39. Maurer, J., and Libchaber, A. Rayleigh-Benard experiment in liquid He: Frequency locking and the onset of turbulence. J. Physicque Lett. (1979) 40:L419-23.
40. Meltzer, D. Explorations in Autism: A Psychoanalytic Study. Perthshire, Scotland: Clunie Press, 1982, pp. 6-32.
41. Metropolis, N., Stein, J., and Stein, P. R. On finite limit sets of transformations on the unit interval. J. Comb. Theor. (1973) A15:25-43.
42. Milnor, J., and Thurston, W. Iterated maps of the interval. Springer. Led. Notes. Math. (1988) 1342: 465-563.
43. Misiurewicz, M., and Szlenk, W. Entropy of piecewise monotone mapping. Studia Math. (1980) 67:45-63.
44. Ornstein, D. S., and Weiss, B. Statistical properties of chaotic systems. Bulletin of the American Mathematical Society (1991) 24:11-116.
45. Oseledec, V. I. A multiplicative ergodic theorm. Lyapounov characteristic numbers for dynamical systems. Transactions of the Moscow Mathematical Society (1968) 197-231.
46. Palis, J., and De Melo, W. Geometric Theory of Dynamical Systems. Springer, 1982.
47. Paulus, M. P., Gass, S.F., Geyer, M. and Mandell, A. J. Ergodic measures of complexity in rat exploratory behavior. Proceedings of the National Academy of Science. (1990) 87:723-7.
48. Paulus, M. P., Gass, S. F., Geyer, M. and Mandell, A. J. A realistic, minimal “middle layer” for neural networks. Physica (1989) D40:135-55.
49. Paulus, M. P., Geyer, M. A., and Mandell, A. J. Statistical mechanics of a neurobiological dynamical system: The spectrum of local entropies s(α) applied to cocaine-perturbed behavior. Physica (1991) A174:567-77.
50. Pesin, YA., B. Lyapounove characteristic exponents and ergodic properties of smooth dynamical systems with invariant measures. Sov. Math. (1976) 17:196-199.
51. Poincaré, H. Les methodes nouvlles de la mecanique celeste, Paris: Gauthieer-Villars, 1899.
52. Polya, G. Induction and Analogy in Mathematics, Vol. 1 Princeton University Press. 1954.
53. Pumpian-Mindlin, E., ed. Psychoanalysis as a Science. Westport, CT: Greenwood, 1952.
54. Reidbord, S., and Redington, D. Psychophysiological processes during insight-oriented therapy. Journal of Nervous and Mental Disease (1992) 180: 649-57.
55. Reynolds, O. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philosophical Transactions of the Royal Society of London, Series A (1895) 186:123-46.
56. Ruelle, D. Thermodynamic Formalism. Addison-Wesley, 1978.
57. Ruelle, D. Ergodic theory of differentiable dynamical systems. Publ. Math. IHES (1979) 50:27-58.
58. Ruelle, D. Chaotic Evolution and Strange Attractors. Cambridge University Press, 1989.
59. Salzman, L. The Obsessive Personality: Origins, Dynamics, and Therapy. New York: Science House, 1968.
60. Schafer, R. A New Language of Psychoanalysis. Yale University Press, 1976.
61. Schafer, R. Conflict as paradoxical actions. Psychoanal. Contemp. Thought (1978) 2:3-24.
62. Schuster, H. G. Deterministic Chaos: An Introduction Weinheim, FRG: VCH, 1989.
63. Sears, R. R., and Wise, G. W. Relations of cup feeding in infancy to thumbsucking and the oral drive. American Journal of Orthopsychiatry (1950) 20: 123-38.
64. Segal, D. S., and Mandell, A. J. Differential behavioral effects of hypothalamic polypeptides. In A.J. Prange, ed., The Thyroid Axis, Drugs and Behavior. Raven Press, 1974, pp. 129-33.
65. Selz, K. A. Mixing properties in human behavioral style and time dependencies in behavior identification: The modeling of a universal dynamical law. Doctoral Dissertation, UMI, New York, 1992.
66. Selz, K.A., and Mandell, A. J. The Bernoulli partition-equivalence of intermittent neuronal discharge patterns. Int. J. Bifurcation Chaos. (1991) 1:717-22.
67. Selz, K. A., and Mandell, A. J. Critical coherence and characteristic times in brain stem neuronal discharge patterns. In J. Davis, J. McKenna, and S. Zornetzer, eds., Single Neuron Computation. 1992, pp. 525-60.
68. Selz, K. A., and Mandell, A. J. Style as mechanism: From man to map of the interval and back. SPIE (1993) 2036: 174-82.
69. Selz, K. A., and Mandell, A. J. A family of autocorrelation graph equivalence classes on symbolic dynamics as models of individual differences in human behavioral style. In R.R. Vallacher and A. J. Nowak, eds., Dynamical Systems in Social Psychology. Academic Press, 1994, pp. 169-97.
70. Smale, S. Differentiable dynamical systems. Bulletin of the American Mathematical Society (1967) 73:747-817.
71. Spitzer, R. L., Williams, J. B. W., Gibbon, M., and First, M. P. SCID-II: Structured Clinical Interview for DSM-III-R Personality Disorders (Version I). American Psychiatric Press, 19909.
72. Swinney, H. L., and Gollub, J. P., eds. Hydrodynamic Instabilities and the Transition to Turbulence. Springer, 1981.
73. Takens, F. Detecting strange attractors in turbulence. Spring, led. Notes. Math. (1980) 898:66-81.
74. Vidal, C, Rous, J. C, Bachelart, S., and Rossi, A. Experimental study of the transition to turbulence in the Belousov-Zhabotinskii reaction. New York Academy of Science (1980) 357:377-96.
75. Whitehead, A. N. Modes of Thought. Free Press-Macmillan, 1938.
76. Wolf, A., Swift, J. R., Swinney, H. L., and Vastano, J. A. Determining Lyapounov exponents from time series. Physica (1985) D16:285-317.