Skiadas C.H., Skiadas C. Chaotic Modelling and Simulation. Analysis of Chaotic Models, Attractors and Forms
Подождите немного. Документ загружается.
314 Chaotic Modelling and Simulation
Dulac, M. H. (1923). Sur les cycles limites. Bull. Soc. Math. Anal. 51, 45–188.
Eckmann, J.-P. (1981). Roads to turbulence in dissipative dynamical systems. Rev.
Mod. Phys. 53, 643–654.
Eckmann, J.-P., H. Koch, and P. Wittwer (1984). A computer-assissted proof of
universality for area-preserving maps. Mem. Am. Math. Soc. 47, 1–122.
Eckmann, J.-P. and D. Ruelle (1985). Ergodic theory of chaos and strange attractors.
Rev. Mod. Phys. 57, 617–656.
Eckmann, J.-P. and P. Wittwer (1987). A complete proof of the Feigenbaum conjec-
tures. J. Stat. Phys. 46, 455–477.
El-Rifai, E. A. and E. Ahmed (1995). Knotted periodic orbits in R
¨
ossler’s equations.
J. Math. Phys. 36(2), 773–777.
Elsner, J. B. and A. A. Tsonis (1992). Nonlinear predicting, chaos and noise. Bull.
Amer. Meteor. Soc. 73, 49–60.
Endler, A. and J. A. C. Gallas (2001). Period four stability and multistability domains
for the H
´
enon map. Physica A 295(1-2), 285–290.
Epstein, H. (1986). New proofs of the existence of the Feigenbaum functions. Comm.
Math. Phys. 106, 395–426.
Epstein, H. R. (1983). Oscillations and chaos in chemical systems. Physica D 7, 47.
Fang, H. P. (1994). Studying the Lorenz equations with one-dimensional maps from
successive local maxima in z. Z. Phys. B 96(4), 547–552.
Farady, M. (1831). On a peculiar class of acoustical figures, and on certain forms
assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. Roy.
Soc. London 121, 299–340.
Fatou, P. (1919). Sur les
´
equations fonctionelles. Bull. Soc. Math. France 47, 161–
271.
Fatou, P. (1920). Sur les
´
equations fonctionelles. Bull. Soc. Math. France 48, 33–94,
208–314.
Fatou, P. (1926). Sur l‘it
´
eration des fonctions transcendentes enti
`
eres. Acta Math. 47,
337–370.
Feichtinger, G. (1992a). Hopf bifurcation in an advertising diffusion model. J. Econ.
Behav. Organ. 17, 401–411.
Feichtinger, G. (1992b). Limit cycles in dynamic economic systems. Ann. Operation
Res. 37, 313–344.
Feichtinger, G., L. L. Ghezzi, and C. Piccardi (1995). Chaotic behavior in an adver-
tising diffusion model. Int. J. of Bifurcation and Chaos 5(1), 255–263.
References 315
Feigenbaum, M. J. (1978). Quantitative universality for a class of nonlinear trans-
formations. J. Stat. Phys. 19, 25–52.
Feigenbaum, M. J. (1979). The universal metric properties of nonlinear transforma-
tions. J. Stat. Phys. 21, 669–706.
Feigenbaum, M. J. (1980a). The metric universal properties of period doubling bi-
furcations and the spectrum for a route to turbulence., Volume 357 of Ann. N. Y.
Acad. Sci. New York: The New York Academy of Sciences.
Feigenbaum, M. J. (1980b). The onset spectrum of turbulence. Phys. Lett. A 74,
375–378.
Feigenbaum, M. J. (1980c). The transition to aperiodic behaviour in turbulent sys-
tems. Commun. Math. Phys. 77, 65–86.
Feigenbaum, M. J. (1980d). Universal behaviour in nonlinear systems. Los Alamos
Science 1, 4–27.
Feigenbaum, M. J. (1983). Universal behavior in nonlinear systems. Physica D 7,
16–39.
Feigenbaum, M. J. (1987a). Scaling spectra and return times of dynamical systems.
J. Stat. Phys. 46, 925–932.
Feigenbaum, M. J. (1987b). Some characterizations of strange sets. J. Stat. Phys. 46,
919–924.
Feigenbaum, M. J. (1988). Presentation functions, fixed points, and a theory of
scaling function dynamics. J. Stat. Phys. 52, 527–569.
Feigenbaum, M. J. (1990). Presentation functions and scaling function theory for
circle maps. In D. K. Campbell (Ed.), Chaos — Soviet American perspectives on
nonlinear science, pp. 3–35. New York: AIP.
Feller, W. (1956). An introduction to probability theory and its applications, Vol-
ume 1. New York: Wiley.
Field, R. J., E. K
¨
or
¨
os, and R. M. Noyes (1972). Oscillations in chemical systems.
II. Thorough analysis of temporal oscillations in the bromate-cerium-malonic acid
system. J. Am. Chem. Soc. 94, 8649–8664.
Field, R. J. and R. M. Noyes (1974). Oscillations in chemical systems. V. quantita-
tive explanation of band migration in the Belousov-Zhabotinskii reaction. J. Am.
Chem. Soc. 96, 2001–2006.
Fisher, R. A. (1937). The wave of advance of advantageous genes. Ann. Eugenics 7,
355–369.
FitzHugh, R. (1969). Mathematical models of excitation and propagation in nerve
and muscle. In H. P. Schwan (Ed.), Biological engineering. New York: McGraw-
Hill.
316 Chaotic Modelling and Simulation
FitzHugh, R. A. (1961). Impulses and physiological states in theoretical models of
nerve membrane. Biophys. J. 1, 445–466.
Flytzanis, N., E. Yiachnakis, and J. Micheloyannis (1991). Analysis of EEG signals
and their spatial correlation over the scalp surface. In M. Markus and A. V. Holden
(Eds.), Nonlinear wave processes in excitable media. New York: Plenum.
Fokas, A. S. and T. Bountis (1996). Order and the ubiquitous occurrence of chaos.
Physica A 228(1-4), 236–244.
Fowler, A. C. and M. J. McGuinness (1982). Hysteresis in the Lorenz equations.
Phys. Lett. A 92, 103.
Fowler, A. C., M. J. McGuinness, and J. D. Gibbon (1982). The complex Lorenz
equations. Physica D 4, 139.
Frank, M., R. Gencay, and T. Stengos (1988). International chaos? Europ. Econ.
Rev. 32, 1569–1584.
Frank, M. and T. Stengos (1988a). The stability of Canadian macroeconomic data as
measured by the largest Lyapunov exponent. Econ. Lett. 27, 11–14.
Frank, M. Z. and T. Stengos (1988b). Chaotic dynamics in economic time-series. J.
Economic Surveys 2, 103–133.
Frank, M. Z. and T. Stengos (1988c). Some evidence concerning macroeconomic
chaos. J. Monetary Economics 22, 423–438.
Frederickson, P., J. L. Kaplan, E. D. Yorke, and Y. J. A. (1983). The Lyapunov
dimension of strange attractors. J. Diff. Eqns. 49, 185–207.
Frouzakis, C. E., R. A. Adomaitis, and I. G. Kevrekidis (1991). Resonance phe-
nomena in an adaptively-controlled system. Int. J. of Bifurcation and Chaos 1(1),
83–106.
Frouzakis, C. E., L. Gardini, I. G. Kevrekidis, G. Millerioux, and C. Mira (1997).
On some properties of invariant sets of two-dimensional noninvertible maps. Int.
J. of Bifurcation and Chaos 7(6), 1167–1194.
Fukuda, W. and S. Katsura (1986). Exactly solvable models showing chaotic behav-
ior II. Physica A 136, 588.
Galias, Z. and P. Zgliczynski (1998). Computer assisted proof of chaos in the Lorenz
equations. Physica D 115, 165–188.
Gallas, J. A. C. (1993). Structure of the parameter space of the H
´
enon map. Phys.
Rev. Lett. 70(18), 2714–2717.
Garbaczewski, P., M. Wolf, and A. Weron (Eds.) (1995). Chaos — The interplay
between stochastic and deterministic behaviour. Proc. of the 31st Winter School of
Theor Phys., Karpasz, Poland, 13.-24. Feb. 1995. Berlin: Springer-Verlag.
References 317
Gause, G. F. and A. A. Witt (1934). On the periodic fluctuations in the numbers
of animals. A mathematical theory of the relaxation interaction between predators
and prey and its application to a population of protozoa. Bull. Acad. Sci. U.R.S.S.,
1551–1559.
Georgiou, I. T. (1999). On the global geometric structure of the dynamics of the
elastic pendulum. Nonlinear Dynamics 18(1), 51–68.
Geysermans, P. and F. Baras (1997). Stochastic description of a period-2 limit cycle.
Europhys. Lett. 40(1), 1–6.
Giovanis, A. and C. H. Skiadas (1995). Forecasting the electricity consumption by
applying stochastic modeling techniques. In J. Janssen, C. H. Skiadas, and C. Zo-
pounidis (Eds.), Advances in stochastic modelling and data analysis. Dordrecht:
Cluwer Acad. Publishers.
Glass, L. (1975). Global analysis of nonlinear chemical kinetics. In B. Berne (Ed.),
Statistical mechanics, pp. 311–349. New York: Plenum.
Glass, L. (1988). Simple mathematical models for complex dynamics in physiologi-
cal systems. In B.-L. Hao (Ed.), Directions in chaos, Volume 2, pp. 90. Singapore:
World Scientific.
Glass, L. (1991). Cardiac arrhythmias and circle maps. Chaos 1, 13–19.
Glass, L., M. R. Guevara, J. Belair, and A. Shrier (1984). Global bifurcations of a
periodically forced biological oscillator. Phys. Rev. A 29, 1348–1357.
Glass, L. and P. Hunter (1990). There is A theory of heart. Physica D 43, 1–16.
Glass, L. and M. C. Mackey (1988). From clocks to chaos. Princeton NJ: Univ.
Press.
Glass, L. and J. S. Pasternack (1978). Stable oscillations in mathematical models of
biological control systems. J. Math. Biol. 6, 207–223.
Glass, L. and R. Young (1979). Structure and dynamics of neural network oscillators.
Brain Res. 179, 207–218.
Glass, L. and W. Zeng (1990). Complex bifurcations and chaos in simple theoretical
models of cardiac oscillations. In Mathematical Approaches to Cardiac Arrhyth-
mias, Volume 591 of Ann. N.Y. Acad. Sci., pp. 316–327.
Gleick, J. (1987). Chaos — Making a new science. New York: Viking.
Goetz, A. (1998). Perturbations of 8-attractors and births of satellite systems. Int. J.
of Bifurcation and Chaos 8(10), 1937–1956.
Gollub, J. P. and H. L. Swinney (1975). Onset of turbulence in a rotating fluid. Phys.
Rev. Lett. 35, 927.
Gompertz, B. (1825). On the nature of the function expressing of the law of human
318 Chaotic Modelling and Simulation
mortality. Philosoph. Trans. Royal Soc. 36, 513–585.
Goriely, A. (1992). From weak to full Painlev
´
e property via time singularities trans-
formations. In T. Bountis (Ed.), Chaotic dynamics and practice. London: Plenum.
Grammaticos, B., B. Dorizzi, and A. Ramani (1983). Integrability of Hamiltonians
with third and fourth degree polynomial potentials. J. Math. Phys. 24, 2289.
Grammaticos, B., A. Ramani, and V. G. Papageorgiou (1991). Do integrable map-
pings have the Painlev
´
e property? Phys. Rev. Lett. 67, 1825.
Grassberger, P. (1981). On the Hausdorff dimension of fractal attractors. J. Stat.
Phys. 26, 173.
Grassberger, P. (1983a). Generalized dimensions of strange attractors. Phys. Lett.
A 97, 227–230.
Grassberger, P. (1983b). On the fractal dimension of the H
´
enon attractor. Phys. Lett.
A 97, 224–226.
Grassberger, P. (1985). Information flow and maximum entropy measures for 1-D
maps. Physica D 14, 365–373.
Grassberger, P. (1986). Toward a quantitative theory of self-generated complexity.
Int. J. Theor. Phys. 25(9), 907–938.
Grassberger, P. and I. Procaccia (1983a). Estimation of the Kolmogorov entropy
from a chaotic signal. Phys. Rev. A 28, 2591–2593.
Grassberger, P. and I. Procaccia (1983b). Measuring the strangeness of strange at-
tractors. Physica D 9, 189–208.
Grassberger, P. and I. Procaccia (1983c). On the characterization of strange attrac-
tors. Phys. Rev. Lett. 50, 346–349.
Grassberger, P. and M. Scheunert (1981). Some more universal scaling laws for
critical mappings. J. Stat. Phys. 26, 697.
Grassberger, P. and T. Schreiber (1999). Statistical mechanics — microscopic chaos
from Brownian motion? Nature 401(6756), 875–876.
Grau, M. and et al (1983). On the periodic orbits of the Contopoulos Hamiltonian.
In L. Garrido (Ed.), Dynamical systems and chaos, Volume 179 of Lecture notes
in physics, pp. 284–286. Berlin: Springer-Verlag.
Grebogi, C., E. Ott, S. Pelikan, and J. A. Yorke (1984). Strange attractors that are
not chaotic. Physica D 13, 261–268.
Grebogi, C., E. Ott, and J. A. Yorke (1982). Chaotic attractors in crisis. Phys. Rev.
Lett. 48, 1507–1510.
Grebogi, C., E. Ott, and J. A. Yorke (1987). Unstable periodic orbits and the dimen-
sion of chaotic attractors. Phys. Rev. A 36, 3522–3524.
References 319
Grebogi, C., E. Ott, and J. A. Yorke (1988). Roundoff induced periodicity and the
correlation dimension of chaotic attractors. Phys. Rev. A 38, 366.
Guckenheimer, J. (1976). A strange strange attractor. In J. E. Marsden and M. Mc-
Cracken (Eds.), The Hopf bifurcation and applications, pp. 368–381. Berlin:
Springer-Verlag.
Guckenheimer, J. (1979a). The bifurcation of quadratic functions. Annals of N.Y.
Acad. Sc. 316, 78–85.
Guckenheimer, J. (1979b). Sensitive dependence to initial conditions for one-
dimensional maps. Commun. Math. Phys. 70, 133.
Guckenheimer, J. (1980a). Dynamics of the van der Pol equation. IEEE Trans. Circ.
and Systems CAS 27, 983.
Guckenheimer, J. (1980b). Symbolic dynamics and relaxation oscillations. Physica
D 1, 227–235.
Guckenheimer, J. and P. J. Holmes (1983). Nonlinear oscillations, dynamical sys-
tems, and bifurcations of vector fields. Berlin: Springer-Verlag.
Guckenheimer, J. and P. J. Holmes (1988). Structurally stable heteroclinic cycles.
Math. Proc. Cambridge Philos. Soc. 103, 189–192.
Guevara, M. R., L. Glass, M. C. Mackey, and A. Shrier (1983). Chaos in neurobiol-
ogy. IEEE Trans. SMC 13, 790.
Hadamard, J. (1898). Les surfaces
`
a courbures oppos
´
ees et leurs lignes g
´
eod
´
esiques.
J. Math. Pure Appl. 4, 27.
Haken, H. (1978). Synergetics; An introduction. New York: Springer-Verlag.
Haken, H. and G. Mayer-Kress (1981). Chapman-Kolmogorov equation and path
integrals for discrete chaos in presence of noise. Z. Physik 43, 185–187.
Hao, B.-L. (Ed.) (1984). Chaos. Singapore: World Scientific.
Hao, B.-L. (Ed.) (1990). Chaos II. Singapore: World Scientific.
Hassard, B., S. P. Hastings, W. C. Troy, and J. Zhang (1994). A computer proof that
the Lorenz equations have “chaotic” solutions. Appl. Math. Lett., in press.
Hausdorff, F. (1919). Dimension und
¨
außeres maß. Math. Annalen 79, 157.
Helleman, R. H. G. (1980a). Nonlinear dynamics, Volume 357 of Ann. N. Y. Acad.
Sci. New York: The New York Academy of Sciences.
Helleman, R. H. G. (1980b). Self-generated chaotic behavior in nonlinear mechan-
ics. In E. G. D. Cohen (Ed.), Fundamental problems in statistical mechanics,
Volume 5, pp. 165. Amsterdam: North-Holland.
Helleman, R. H. G. (1981). One mechanism for the onsets of largescale chaos in con-
320 Chaotic Modelling and Simulation
servative and dissipative systems. In W. H. et al. (Ed.), Nonequilibrium problems
in statistical mechanics, Volume 2. New York: Wiley.
Helleman, R. H. G. (1984). Feigenbaum sequences in conservative and dissipative
systems. Springer Ser. in Synerg. 11.
H
´
enon, M. (1969). Numerical study of quadratic area-preserving mappings. Quart.
Appl. Math. 27, 291–312.
H
´
enon, M. (1976). A two-dimensional mapping with a strange attractor. Commun.
Math. Phys. 50, 69–77.
H
´
enon, M. (1982). On the numerical computation of Poincar
´
e maps. Physica D 5,
412–414.
H
´
enon, M. (1989). Chaotic scattering modelled by an inclined billiard. Physica
D 33, 132–156.
H
´
enon, M. and C. Heiles (1964). The applicability of the third integral of motion:
Some numerical experiments. Astron. J. 69, 73–79.
H
´
enon, M. and Y. Pomeau (1977). Two strange attractors with a simple structure. In
R. Temam (Ed.), Turbulence and Navier-Stokes equations, Volume 565 of Lecture
notes in mathematics, pp. 29. Berlin: Springer-Verlag.
Hilborn, R. C. (1994). Chaos and nonlinear dynamics: an introduction for scientists
and engineers. Oxford New York: Oxford Univ. Press.
Hirsch, M. W. and S. Smale (1974). Differential equations, dynamical systems, and
linear algebra. New York: Academic Press.
Hodgkin, A. L. and A. F. Huxley (1952a). Current carried by sodium and potassium
ions through the membrane of the giant axon of loligo. J. Physiology 116, 449–
472.
Hodgkin, A. L. and A. F. Huxley (1952b). A quantitative description of membrane
current and its application to conduction and excitation in nerve. J. Physiol. 116,
500–544.
Holmes, C. and P. J. Holmes (1981). Second order averaging and bifurcations to
subharmonics in Duffing’s equation. J. Sound Vib. 78, 161–174.
Holmes, P. J. (1977a). Behavior of an oscillator with even nonlinear damping. Int. J.
Nonlinear Mech. 12, 323–326.
Holmes, P. J. (1977b). Strange phenomena in dynamical systems and their physical
implications. Applied Mathematical Modelling 7(1), 362–366.
Holmes, P. J. (1979a). A nonlinear oscillator with a strange attractor. Phil. Trans.
Roy. Soc. London 292, 419–448.
Holmes, P. J. (1979b). Recurrent periodic and nonperiodic behavior in simple dy-
References 321
namical systems. In Proc. Joint National Meeting, pp. 107.
Holmes, P. J. (1980). Periodic, non-periodic and irregular motions in a Hamiltonian
system. Rocky Mountain J. Math 10(4), 679–693.
Holmes, P. J. (1982). Proof of non-integrability for the H
´
enon-Heiles Hamiltonian
near an exceptional integrable case. Physica D 5, 35–347.
Holmes, P. J. (1984). Bifurcation sequences in horseshoe maps: infinitely many
routes to chaos. Phys. Lett. 104A, 299–302.
Holmes, P. J. (1986). Spatial structure of time-periodic solutions of the Ginzburg-
Landau equation. Physica D 23, 4–90.
Holmes, P. J. (1990). Poincar
´
e, celestial mechanics, dynamical systems theory and
“chaos”. Physics Reports 193(3), 137–163.
Holmes, P. J. and J. E. Marsden (1982). Horseshoes in perturbations of Hamiltonian
systems with two degrees of freedom. Comm. Math. Phys. 82, 523–544.
Holmes, P. J. and D. A. Rand (1976). The bifurcations of Duffing’s equation: An
application of catastrophy theory. J. Sound Vib. 44(2), 237–253.
Holmes, P. J. and D. A. Rand (1978). Bifurcation of the forced van der Pol oscillator.
Quart. Appl. Math. 35, 495–509.
Hopf, E. (1942). Abzweigung einer periodischen L
¨
osung von einer station
¨
aren
L
¨
osung eines differentialsystems. Ber. Math.-Phys. Akad. Wiss. Leipz. 94, 3–22.
Hopf, E. (1948). A mathematical example displaying features of turbulence (ex-
cerpt). Commun. Pure Appl. Math. 1, 303.
Hopf, F. A., D. L. Kaplan, H. M. Gibbs, and R. L. Shoemaker (1982). Bifurcations
to chaos in optical bistability. Phys. Rev. A 25, 2172.
Hoppensteadt, F. C. (1993). Analysis and simulation of chaotic systems. New York:
Springer-Verlag.
Hudson, J. L., O. E. R
¨
ossler, and H. C. Killory (1988). Chaos in a four-variable
piecewise-linear system of differential equations. IEEE Trans. Circ. and Systems
CAS 35, 902–908.
Hunter, C. and A. Toomre (1969). Dynamics of the bending of the galaxy. Astrophys.
J. 155, 747.
Ide, K. and S. Wiggins (1989). The bifurcation to homoclinic tori in the quasiperi-
odically forced Duffing oscillator. Physica D 34, 169–182.
Ikeda, K. (1979). Multiple-valued stationary state and its instability of the transmit-
ted light by a ring cavity system. Opt. Commun. 30, 257.
Ikeda, K. and O. Akimoto (1982). Instability leading to periodic and chaotic self-
pulsations in a bistable optical cavity. Phys. Rev. Lett. 48, 617.
322 Chaotic Modelling and Simulation
Ikeda, K., H. Daido, and O. Akimoto (1980). Optical turbulence: Chaotic behavior
of transmitted light from a ring cavity. Phys. Rev. Lett. 45, 709.
Ikeda, K. and K. Kondo (1982). Successive higher-harmonic bifurcations in systems
with delayed feedback. Phys. Rev. Lett. 49, 1467.
Ikeda, K. and K. Matsumoto (1987). High-dimensional chaotic behavior in systems
with time-delayed feedback. Physica D 29, 223–235.
Ikeda, T. and S. Murakami (1999). Dynamic response and stability of a rotating
asymmetric shaft mounted on a flexible base. Nonlinear Dynamics 20(1), 1–19.
Ikeda, Y. and S. Tokinaga (2000). Approximation of chaotic dynamics by using
smaller number of data based upon the genetic programming and its applications.
IEICE Trans. Fund. Elec. Com. Com. E83A(8), 1599–1607.
Iooss, G., R. Helleman, and R. Stora (Eds.) (1983). Chaotic behavior of deterministic
systems. Amsterdam: North Holland.
Ishida, Y., T. Ikeda, T. Yamamoto, and S. Murakami (1989). Nonstationary vibration
of a rotating shaft with nonlinear spring characteristics during acceleration through
a critical speed (A critical speed of a 1/2-order subharmonic oscillation). JSME
Int. J. Ser. III 32(4), 575–584.
Ito, A. (1979). Successive subharmonic bifurcations and chaos in a nonlinear Math-
ieu equation. Prog. Theor. Phys. 61, 815.
Ito, H. and L. Glass (1991). Spiral breakup in a new model of discrete excitable
media. Phys. Rev. Lett. 66, 671–674.
Itoh, H. (1985). Nonintegrability of H
´
enon-Heiles system and a theorem of ziglin.
Kodai Math. J. 8, 120.
Joy, M. P. (1995). On the bifurcation in a modulated logistic map: Comment. Phys.
Lett. A 202(2-3), 237–239.
Julia, G. (1918). M
´
emoire sur l’it
´
eration des fonctions rationelles. J. Math. Pure
Appl. 8, 47–245.
Kac, M. (1947). Random walk and the theory of Brownian motion. Am. Math.
Month. 54(7), 369–391.
Kadanoff, L. P. (1981). Scaling for a critical Kolmogorov-Arnold-Moser trajectory.
Phys. Rev. Lett. 47, 1641–1643.
Kadanoff, L. P. (1993). From order to chaos: Essays: Critical, chaotic and other-
wise. Singapore: World Scientific.
Kahlert, C. and O. E. R
¨
ossler (1984). Chaos as a limit in a boundary value problem.
Z. Naturforsch. A 39, 1200–1203.
Kahlert, C. and O. E. R
¨
ossler (1985). Analytical properties of Poincar
´
e half-maps in
References 323
a class of piecewise-linear dynamical systems. Z. Naturforsch. 40, 1011–1025.
Kahlert, C. and O. E. R
¨
ossler (1986). The separating mechanisms in Poincar
´
e half-
maps. Z. Naturforsch. A 41, 1369–1380.
Kahlert, C. and O. E. R
¨
ossler (1987). Analogues to a boundary away from analyticity.
Z. Naturforsch. 42, 324–328.
Kalman, R. E. (1956). Nonlinear aspects of sample data control systems. In Proc.
Symp. on Nonlin. Circ. Anal., Brooklyn, April 1956, pp. 273–313.
Kalman, R. E. (1960). A new approach to linear filtering and prediction problems.
J. Basic Eng. 82, 35–45.
Kapitaniak, T. (1990). Analytical condition for chaotic behavior of the Duffing os-
cillator. Phys. Lett. A 144, 322–324.
Kapitaniak, T. (1991). On strange non-chaotic attractors and their dimension. Chaos
Solitons and Fractals 1, 67–77.
Kaplan, H. (1983). New method for calculating stable and unstable periodic orbits
of one-dimensional maps. Phys. Lett. A 97, 365.
Kaplan, J. L. and J. A. Yorke (1979a). Chaotic behavior of multidimensional dif-
ference equations. In H. O. Walter and H.-O. Peitgen (Eds.), Functional differen-
tial equations and approximation of fixed points, Volume 730 of Lecture notes in
mathematics, pp. 204–227. Berlin: Springer-Verlag.
Kaplan, J. L. and J. A. Yorke (1979b). The onset of chaos in a fluid flow model of
Lorenz, Volume 316 of Ann. N. Y. Acad. Sci. New York: The New York Academy
of Sciences.
Kappos, E. (1996). The Conley index and global bifurcations. II. Illustrative appli-
cations. J. of Bifurcation and Chaos 6(12B), 2491–2505.
Karamanos, K. and G. Nicolis (1999). Symbolic dynamics and entropy analysis of
Feigenbaum limit sets. Chaos Solitons Fractals 10(7), 1135–1150.
K
´
arolyi, G., I. Scheuring, and T. Cz
´
ar
´
an (2002). Metabolic network dynamics in
open chaotic flow. Chaos 12(2), 460–469.
K
´
arolyi, G. and T. T
´
el (1997). Chaotic tracer scattering and fractal basin boundaries
in a blinking vortex-sink system. Physics Reports 290, 125–147.
Katsamaki, A. and C. H. Skiadas (1995). Analytic solution and estimation of para-
meters on a stochastic exponential model for a technological diffusion process.
Appl. Stoch. Mod. Dat. Analys. 11, 59–75.
Katz, L. (1996). Note on the Schwarzian derivative. Chaos Solitons Fractals 7(9),
1495–1496.
Keppenne, C. and C. Nicolis (1988). Toward a quantitative view of predictability of