메뉴 건너뛰기




Volumn 7, Issue 1, 1997, Pages 67-81

Entropy conservation as hr -X1d1 in neurobiological dynamical systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0001977318     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166241     Document Type: Article
Times cited : (19)

References (62)
  • 2
    • 0024938193 scopus 로고
    • A realistic, minimal "middle layer" for neural networks
    • M. P. Paulus, S. F. Gass, and A. J. Mandell, "A realistic, minimal "middle layer" for neural networks," Physica D 40, 135-155 (1989).
    • (1989) Physica D , vol.40 , pp. 135-155
    • Paulus, M.P.1    Gass, S.F.2    Mandell, A.J.3
  • 3
    • 0000252317 scopus 로고
    • Obstructions to shadowing when a Lyapunov exponent fluctuates about zero
    • S. Dawson, C. Grebogi, T. Sauer, and J. A. Yorke, "Obstructions to shadowing when a Lyapunov exponent fluctuates about zero," Phys. Rev. Lett. 73, 1927-1931 (1994).
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 1927-1931
    • Dawson, S.1    Grebogi, C.2    Sauer, T.3    Yorke, J.A.4
  • 4
    • 0010198361 scopus 로고
    • Bernoulli partition-equivalence of intermittent neuronal discharge patterns
    • K. A. Selz and A. J. Mandell, "Bernoulli partition-equivalence of intermittent neuronal discharge patterns," Int. J. Bifurcation Chaos 1,717-722 (1991).
    • (1991) Int. J. Bifurcation Chaos , vol.1 , pp. 717-722
    • Selz, K.A.1    Mandell, A.J.2
  • 5
    • 1442347069 scopus 로고
    • Distribution of local Mandelbrot-Hurst exponents: Motor activity in cocaine treated fetal rats and manic depressive patients
    • K. A. Selz, A. J. Mandell, C. A. Anderson, W. Smotherman, and M. Teicher, ' 'Distribution of local Mandelbrot-Hurst exponents: Motor activity in cocaine treated fetal rats and manic depressive patients," Fractals 3, 893-904 (1995).
    • (1995) Fractals , vol.3 , pp. 893-904
    • Selz, K.A.1    Mandell, A.J.2    Anderson, C.A.3    Smotherman, W.4    Teicher, M.5
  • 6
    • 35949018382 scopus 로고
    • Ergodic theory of chaos and strange attractors
    • J. P. Eckmann and D. Ruelle, "Ergodic theory of chaos and strange attractors," Rev. Mod. Phys. 57, 616-656 (1985).
    • (1985) Rev. Mod. Phys. , vol.57 , pp. 616-656
    • Eckmann, J.P.1    Ruelle, D.2
  • 7
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • S. Smale, "Differentiable dynamical systems," Bull. Am. Math. Soc. 73, 747-817 (1967).
    • (1967) Bull. Am. Math. Soc. , vol.73 , pp. 747-817
    • Smale, S.1
  • 8
    • 84968507653 scopus 로고
    • Dynamical systems, filtrations and entropy
    • M. Shub, "Dynamical systems, filtrations and entropy," Bull. Am. Math. Soc. 80, 27-41 (1974).
    • (1974) Bull. Am. Math. Soc. , vol.80 , pp. 27-41
    • Shub, M.1
  • 9
    • 84961291543 scopus 로고
    • Characteristic Lyapunov exponents and smooth ergodic theory
    • Ya. B. Pesin, "Characteristic Lyapunov exponents and smooth ergodic theory," Russ. Math. Surveys 32, 55-114 (1977).
    • (1977) Russ. Math. Surveys , vol.32 , pp. 55-114
    • Pesin, Y.B.1
  • 11
    • 0002564801 scopus 로고
    • Geodesic flows on closed Riemannian manifolds with negative curvature
    • D. V. Anosov, "Geodesic flows on closed Riemannian manifolds with negative curvature," Proc. Steklov Inst. Mat. 90, 1-235 (1967).
    • (1967) Proc. Steklov Inst. Mat. , vol.90 , pp. 1-235
    • Anosov, D.V.1
  • 12
    • 0001441814 scopus 로고
    • General theory of dynamical systems and classical mechanics
    • North Holland, Amsterdam
    • A. N. Kolmogorov, "General theory of dynamical systems and classical mechanics," Proceedings of the International Congress on Mathematics (North Holland, Amsterdam, 1957) pp. 315-333.
    • (1957) Proceedings of the International Congress on Mathematics , pp. 315-333
    • Kolmogorov, A.N.1
  • 13
    • 0040397974 scopus 로고
    • Dynamical systems with countably-multiple Legesgue spectrum
    • Ya. G. Sinai, "Dynamical systems with countably-multiple Legesgue spectrum," Am. Math. Soc. Transi. 68, 34-88 (1970).
    • (1970) Am. Math. Soc. Transi. , vol.68 , pp. 34-88
    • Sinai, Y.G.1
  • 14
    • 0000543733 scopus 로고
    • A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems
    • V. I. Oseledec, "A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical systems," Trans. Moscow Math. Soc. 19, 197-231 (1968).
    • (1968) Trans. Moscow Math. Soc. , vol.19 , pp. 197-231
    • Oseledec, V.I.1
  • 16
    • 0039476596 scopus 로고
    • Applications of ergodic theory to the investigation of manifolds of negative curvature
    • G. A. Margulis, "Applications of ergodic theory to the investigation of manifolds of negative curvature," Funk. Anal. Ego Pril. 3, 89-90 (1969).
    • (1969) Funk. Anal. Ego Pril. , vol.3 , pp. 89-90
    • Margulis, G.A.1
  • 18
    • 0001743663 scopus 로고
    • Fractal time in condensed matter
    • M. F. Shlesinger, "Fractal time in condensed matter," Ann. Rev. Phys. Chem. 39, 269-290 (1988).
    • (1988) Ann. Rev. Phys. Chem. , vol.39 , pp. 269-290
    • Shlesinger, M.F.1
  • 19
    • 0003586464 scopus 로고
    • Plenum Press, New York
    • J. Feder, Fractals (Plenum Press, New York, 1988).
    • (1988) Fractals
    • Feder, J.1
  • 21
    • 33749611625 scopus 로고
    • Puttermesser and Xanthippe
    • Knopf, New York
    • C. Ozick, "Puttermesser and Xanthippe," in Lévitation: Five Fictions (Knopf, New York, 1982).
    • (1982) Lévitation: Five Fictions
    • Ozick, C.1
  • 22
    • 0001085798 scopus 로고
    • Zêta functions for expanding maps and Anosov flows
    • D. Ruelle, "Zêta functions for expanding maps and Anosov flows," Invent. Math. 34, 231-242 (1976).
    • (1976) Invent. Math. , vol.34 , pp. 231-242
    • Ruelle, D.1
  • 23
    • 33646861537 scopus 로고
    • Renewal theorems in symbolic dynamics with applications to geodesic flows, non-Euclidean tesselations and their fractal limit sets
    • S. Lalley, "Renewal theorems in symbolic dynamics with applications to geodesic flows, non-Euclidean tesselations and their fractal limit sets," Acta Math. 163, 1-55 (1990).
    • (1990) Acta Math. , vol.163 , pp. 1-55
    • Lalley, S.1
  • 24
    • 0001887299 scopus 로고
    • Approach to equilibrium for locally expanding maps in R
    • D. Mayer, "Approach to equilibrium for locally expanding maps in R," Commun. Math. Phys. 95, 1-15 (1984).
    • (1984) Commun. Math. Phys. , vol.95 , pp. 1-15
    • Mayer, D.1
  • 25
    • 0000496951 scopus 로고
    • An analogue of the Prime Number Theorem for closed orbits of Axiom a flows
    • W. Parry, and M. Pollicott, "An analogue of the Prime Number Theorem for closed orbits of Axiom A flows," Ann. Math. 118, 573-591 (1983).
    • (1983) Ann. Math. , vol.118 , pp. 573-591
    • Parry, W.1    Pollicott, M.2
  • 26
    • 0002869924 scopus 로고
    • On periodic points
    • E. Artin and B. Mazur, "On periodic points," Ann. Math. 81, 82-99 (1965).
    • (1965) Ann. Math. , vol.81 , pp. 82-99
    • Artin, E.1    Mazur, B.2
  • 28
    • 0003288329 scopus 로고    scopus 로고
    • Topological entropy and equivalence of dy-namical systems
    • R. Adler and B. Marcus, "Topological entropy and equivalence of dy-namical systems," Mem. Amer. Math Soc. #219 (1979).
    • Mem. Amer. Math Soc. # , vol.219 , pp. 1979
    • Adler, R.1    Marcus, B.2
  • 29
    • 51649149112 scopus 로고
    • Volume growth and entropy
    • Y. Yomdin, "Volume growth and entropy," Israel J. Math. 57, 285-301 (1987).
    • (1987) Israel J. Math. , vol.57 , pp. 285-301
    • Yomdin, Y.1
  • 30
    • 0000097875 scopus 로고
    • Symbolic dynamics and hyperbolic dynamical systems
    • V. M. Alexeev and M. V. Jacobson, "Symbolic dynamics and hyperbolic dynamical systems," Phys. Rep. 75, 287-325 (1981).
    • (1981) Phys. Rep. , vol.75 , pp. 287-325
    • Alexeev, V.M.1    Jacobson, M.V.2
  • 32
    • 0001745950 scopus 로고
    • Classification of subshifts of finite type
    • R. F. Williams, "Classification of subshifts of finite type," Ann. Math. 98, 120-153 (1973).
    • (1973) Ann. Math. , vol.98 , pp. 120-153
    • Williams, R.F.1
  • 33
    • 0001440467 scopus 로고
    • Factors and extensions to full shifts
    • B. Marcus, "Factors and extensions to full shifts," Monatsheft. Math. 88, 239-247 (1979).
    • (1979) Monatsheft. Math. , vol.88 , pp. 239-247
    • Marcus, B.1
  • 35
    • 0001485296 scopus 로고
    • On the relations among various entropy characteristics of dynamical systems
    • E. I. Dinaburg, "On the relations among various entropy characteristics of dynamical systems," Math. USSR-Izv. 5, 337-378 (1971).
    • (1971) Math. USSR-Izv. , vol.5 , pp. 337-378
    • Dinaburg, E.I.1
  • 36
  • 37
    • 0040394687 scopus 로고
    • A relation between Lyapunov exponents, Hausdorff dimension and entropy
    • A. Manning, "A relation between Lyapunov exponents, Hausdorff dimension and entropy," Ergod. Theor. Dyn. Syst. l, 451-459 (1981).
    • (1981) Ergod. Theor. Dyn. Syst. L , pp. 451-459
    • Manning, A.1
  • 38
    • 0002822757 scopus 로고
    • Preturbulence: A region observed in a fluid now model of Lorenz
    • J. L. Kaplan and J. A. Yorke, "Preturbulence: a region observed in a fluid now model of Lorenz," Commun. Math. Phys. 67, 93-104 (1979).
    • (1979) Commun. Math. Phys. , vol.67 , pp. 93-104
    • Kaplan, J.L.1    Yorke, J.A.2
  • 39
    • 2042472054 scopus 로고
    • On the dimension of attractors of k-contracting systems in an infinite dimensional space
    • Ya. S. Ilyashenko, "On the dimension of attractors of k-contracting systems in an infinite dimensional space," Vestr. Mosk. Univ. Ser. 1, Mat. Mech. 3, 52-58 (1983).
    • (1983) Vestr. Mosk. Univ. Ser. 1, Mat. Mech. , vol.3 , pp. 52-58
    • Ilyashenko, Y.S.1
  • 41
    • 1842443477 scopus 로고
    • Dynamical entropy is conserved in cocaine-induced changes in fetal rat motoric patterns
    • W. P. Smotherman, K. A. Selz, and A. J. Mandell, "Dynamical entropy is conserved in cocaine-induced changes in fetal rat motoric patterns," Psychoneuroendocrinology 20, 31-46 (1995).
    • (1995) Psychoneuroendocrinology , vol.20 , pp. 31-46
    • Smotherman, W.P.1    Selz, K.A.2    Mandell, A.J.3
  • 42
    • 0020841067 scopus 로고
    • From intermittency to transitivity in neuropsychobiological flows
    • A. J. Mandell, "From intermittency to transitivity in neuropsychobiological flows," Am. J. Physiol. 245, R484-R494 (1983).
    • (1983) Am. J. Physiol. , vol.245
    • Mandell, A.J.1
  • 43
    • 0021287508 scopus 로고
    • Non-equilibrium behavior of some brain enzyme and receptor systems
    • A. J. Mandell, "Non-equilibrium behavior of some brain enzyme and receptor systems," Ann. Rev. Pharmacol. Toxicol. 24, 237-274 (1984).
    • (1984) Ann. Rev. Pharmacol. Toxicol. , vol.24 , pp. 237-274
    • Mandell, A.J.1
  • 44
    • 45949127771 scopus 로고
    • Different ways to turbulence in dissipative dynamical systems
    • P. Manneville and Y. Pomeau, "Different ways to turbulence in dissipative dynamical systems," Physica D l, 219-232 (1980).
    • (1980) Physica D , vol.50 , pp. 219-232
    • Manneville, P.1    Pomeau, Y.2
  • 45
    • 12044255333 scopus 로고
    • On-off intermittency: A mechanism for bursting
    • N. Platt, E. S. Spiegel, and C. Tresser, "On-off intermittency: a mechanism for bursting," Phys. Rev. Lett. 70, 279-283 (1993).
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 279-283
    • Platt, N.1    Spiegel, E.S.2    Tresser, C.3
  • 46
    • 0001042825 scopus 로고
    • Accelerated diffusion in Josephson Junctions and related chaotic systems
    • T. Geisel, J. Nienvetberg, and A. Zacherl, "Accelerated diffusion in Josephson Junctions and related chaotic systems," Phys. Rev. Lett. 5-4,616-670 (1985).
    • (1985) Phys. Rev. Lett. , vol.5 , pp. 616-670
    • Geisel, T.1    Nienvetberg, J.2    Zacherl, A.3
  • 47
    • 0000592962 scopus 로고
    • Comment on 'Accelerated diffusion in Josephson Junctions and related chaotic systems'
    • M. F. Shlesinger and J. Klafter, "Comment on 'Accelerated diffusion in Josephson Junctions and related chaotic systems'," Phys. Rev. Lett. 54, 2551 (1985).
    • (1985) Phys. Rev. Lett. , vol.54 , pp. 2551
    • Shlesinger, M.F.1    Klafter, J.2
  • 48
    • 0000307960 scopus 로고
    • Sporadicity: Between periodic and chaotic dynamical behaviors
    • P. Gaspard and X.-J. Wang, "Sporadicity: Between periodic and chaotic dynamical behaviors," Proc. Natl. Acad. Sei. USA 85, 4591-4595 (1988).
    • (1988) Proc. Natl. Acad. Sei. USA , vol.85 , pp. 4591-4595
    • Gaspard, P.1    Wang, X.-J.2
  • 49
    • 0008494528 scopus 로고
    • Determining Lyapunov spectra from a time series
    • A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, "Determining Lyapunov spectra from a time series," Physica D 16, 285-317 (1985).
    • (1985) Physica D , vol.16 , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vastano, J.A.4
  • 51
    • 40749093037 scopus 로고
    • Measuring the strangeness of strange attractors
    • P. Grassberger and I. Proccacia, "Measuring the strangeness of strange attractors," Physica D 9, 189-208 (1983).
    • (1983) Physica D , vol.9 , pp. 189-208
    • Grassberger, P.1    Proccacia, I.2
  • 52
    • 0000822478 scopus 로고
    • Plateau onset for correlation dimension: When does it occur?
    • M. Ding, C. Grebogi, E. Ott, T. Sauer, and J. Yorke, "Plateau onset for correlation dimension: When does it occur?" Phys. Rev. Lett. 70, 3872-3875 (1993)
    • (1993) Phys. Rev. Lett. , vol.70 , pp. 3872-3875
    • Ding, M.1    Grebogi, C.2    Ott, E.3    Sauer, T.4    Yorke, J.5
  • 53
    • 0023386145 scopus 로고
    • Dynamical complexity and pathological order in the cardiac monitoring problem
    • A. J. Mandell, "Dynamical complexity and pathological order in the cardiac monitoring problem," Physica D 27, 235-242 (1987).
    • (1987) Physica D , vol.27 , pp. 235-242
    • Mandell, A.J.1
  • 56
    • 0000009894 scopus 로고
    • Preserving chaos: Control strategies to preserve complex dynamics with potential relevance to biological disorders
    • W. Yang, M. Ding, A. J. Mandell, and E. Ott, "Preserving chaos: control strategies to preserve complex dynamics with potential relevance to biological disorders," Phys. Rev. E 51, 102-110 (1995).
    • (1995) Phys. Rev. e , vol.51 , pp. 102-110
    • Yang, W.1    Ding, M.2    Mandell, A.J.3    Ott, E.4
  • 57
    • 0026754196 scopus 로고
    • Childhood medical and behavioral consequences of maternal cocaine use
    • L. Singer, K. Farkas, and R. Kliegman, "Childhood medical and behavioral consequences of maternal cocaine use," J. Pédiatrie Psychol. 17, 389-406 (1992).
    • (1992) J. Pédiatrie Psychol. , vol.17 , pp. 389-406
    • Singer, L.1    Farkas, K.2    Kliegman, R.3
  • 58
    • 0021646466 scopus 로고
    • P-300 studies with cocaine in man
    • edited by J. Grabowski, NIDA Res. Monogr.
    • R. T. Jones, "P-300 studies with cocaine in man," in Cocaine: Pharmacology, Effects and Treatment of Abuse, edited by J. Grabowski, NIDA Res. Monogr. 50, 34-54 (1984).
    • (1984) Cocaine: Pharmacology, Effects and Treatment of Abuse , vol.50 , pp. 34-54
    • Jones, R.T.1
  • 60
    • 28044454209 scopus 로고
    • Evidence for synergetic dynamics in a mammalian pituitary cell perifusion system
    • edited by E. Basar, H. Flohr, H. Haken, and A. J. Mandell Springer-Verlag, New York
    • R. C. Guillemin, P. Brazeau, A. Briskin, and A. J. Mandell, "Evidence for synergetic dynamics in a mammalian pituitary cell perifusion system," in Synergetics of Brain, edited by E. Basar, H. Flohr, H. Haken, and A. J. Mandell (Springer-Verlag, New York, 1983) pp. 155-162.
    • (1983) Synergetics of Brain , pp. 155-162
    • Guillemin, R.C.1    Brazeau, P.2    Briskin, A.3    Mandell, A.J.4
  • 61
    • 84989024074 scopus 로고
    • The hyperbolic helix hypothesis
    • edited by L. Pietronero and E. Tosatti Eisevier Science, New York
    • A. J. Mandell, "The hyperbolic helix hypothesis," in Fractals in Pliysics, edited by L. Pietronero and E. Tosatti (Eisevier Science, New York, 1986), pp. 469-474.
    • (1986) Fractals in Pliysics , pp. 469-474
    • Mandell, A.J.1
  • 62
    • 0026015905 scopus 로고
    • Approximate entropy as a measure of system complexity
    • S. M. Pincus, "Approximate entropy as a measure of system complexity," Proc. Natl. Acad. Sei. USA 88, 2297-2301 (1991).
    • (1991) Proc. Natl. Acad. Sei. USA , vol.88 , pp. 2297-2301
    • Pincus, S.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.