Temporal Disorder in Human Oscillatory Systems: Proceedings by Professor Dr. Ludger Rensing, Professor Dr. Uwe an der

By Professor Dr. Ludger Rensing, Professor Dr. Uwe an der Heiden, Professor Dr. Michael C. Mackey (auth.)

Rhythms of the guts and of the anxious and endocrine procedure, respiring, locomotory routine, sleep, circadian rhythms and tissue telephone cycles are significant parts of the temporal order of guy. The dynamics of those platforms are characterised by way of adjustments within the homes of an oscillator, transitions from oscillatory states into chaotic or desk bound states, and vice versa, coupling or uncoupling among or extra oscillators. Any deviation from the conventional variety to both kind of ordered states could be outlined as temporal illness. Pathological adjustments of temporal association, resembling tremor, epileptic seizures, Cheyne-Stokes respiring, cardiac arrhythmicities and circadian desynchronization, will be because of small alterations within the order (control) parameters. One significant point of the symposium used to be the research of attribute positive aspects of those temporal keep watch over structures, together with nonlinear dynamics of interactions, confident, unfavourable and combined suggestions platforms, temporal delays, and their mathematical description and modelling. the final word target is a greater knowing of the rules of temporal association so as to deal with periodic illnesses or different perturbations of "normal" dynamics in human oscillatory systems.

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Temporal Disorder in Human Oscillatory Systems: Proceedings of an International Symposium University of Bremen, 8–13 September 1986

Rhythms of the center and of the worried and endocrine procedure, respiring, locomotory hobbies, sleep, circadian rhythms and tissue cellphone cycles are significant parts of the temporal order of guy. The dynamics of those structures are characterised via adjustments within the houses of an oscillator, transitions from oscillatory states into chaotic or desk bound states, and vice versa, coupling or uncoupling among or extra oscillators.

Extra info for Temporal Disorder in Human Oscillatory Systems: Proceedings of an International Symposium University of Bremen, 8–13 September 1986

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Math. BioI. D. H. Renninger: J. Math. BioI. M. 13 (Amer. Math. Soc. 1980~ --- ---- 20. C. Mackey, L. Glass: Science 197, 287 (1977) 21. R. D. Barchas, B. Huberman: In Synergetics of the Brain, ed. by E. Basar, H. Flohr, H. J. Mandell, Springer Ser. , Vol. 23 (Springer, Berlin, Heidelberg 1983) 22. U. C. -O. Walther: In Mathematical Aspects of Physiology, ed. C. Hoppensteadt, Lect. Appl. Math. 19 (Amer. Math. , Providence, Rhode Island 1981) 23. C. Mackey, U. an der Heiden: J. Math. BioI. 19, 211 (1984) 24.

6a) (exponential decrease to 0) holds if, in the time between t-1 and t-1, the values of x are larger than 1 or smaller than b. (6b) (exponential increase to y) whenever, in the time interval from i-1 to t-1, the values of x are between b and 1. Thus any solution of Eq. (6b) takes place at any time t if, at time t*-1, the variable x(t) crosses the level b or 1. (S), and illustrate this pattern. For simplicity, we restrict our attention to the case b = 1/2 and a fixed ratio y = 2. Some remarks for arbitrary parameters are given in the end of this section.

BioI. D. H. Renninger: J. Math. BioI. M. 13 (Amer. Math. Soc. 1980~ --- ---- 20. C. Mackey, L. Glass: Science 197, 287 (1977) 21. R. D. Barchas, B. Huberman: In Synergetics of the Brain, ed. by E. Basar, H. Flohr, H. J. Mandell, Springer Ser. , Vol. 23 (Springer, Berlin, Heidelberg 1983) 22. U. C. -O. Walther: In Mathematical Aspects of Physiology, ed. C. Hoppensteadt, Lect. Appl. Math. 19 (Amer. Math. , Providence, Rhode Island 1981) 23. C. Mackey, U. an der Heiden: J. Math. BioI. 19, 211 (1984) 24.

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