where m is the Lebesgue measure of R, has a fixed density f∗. This fixed density gives rise to a physical measure of S, which describes the asymptotic behavior of the chaotic orbits from the statistical viewpoint [3]. Our purpose is efficient computation of such fixed densities. In his book [6], Ulam proposed a piecewise constant approximation method to calculate the fixed density f∗ and conjec...

Given K real d-by-d nonsingular matrices S 1, . . . , S K , by extending the well-known Li-Yorke chaotic description of a deterministic nonlinear dynamical system to a discrete-time linear inclusion dynamical system: xn ∈ {S k xn−1}1≤k≤K with x0 ∈ Rd and n ≥ 1, we study the chaotic characteristic of the state trajectory (xn(x0, σ))n≥1, governed by a switching law σ : N → {1, . . . , K}, for any...

in order to fabrication of transparent glass-ceramics with li-mica nano crystals, the glasses with chemical composition of 94.9 mass% li(1+x)mg3alsi3(1+x)f2 (x=0.5) with 5.1 mass% mgf2 were crystallized. the glasses were fabricated via the conventional melt-quenching technique. mica crystals were precipitated in the glass phase by later heat treatment. glass samples had glass transition tempera...

in this research prediction methods of artificial neural network and chaos theory are employed to predict daily, weekly and monthly runoff. for this, runoff series data observed at pole-kohneh located in the qareh-soo river. the nonlinear predictions of chaos are found to be in close agreement with the observed runoff, with high correlation coefficient for daily and weekly time scales. predicte...

Ying-Cheng Lai,1,* Celso Grebogi,2,3,† James A. Yorke,3,‡ and S. C. Venkataramani2 1Departments of Physics and Astronomy and Mathematics, The University of Kansas, Lawrence, Kansas 66045 2Institute for Plasma Research, The University of Maryland, College Park, Maryland 20742 3Department of Mathematics, Institute for Physical Science and Technology, The University of Maryland, College Park, Mary...

We consider a family of scalar delay differential equations x(t) = f(t, xt), with a nonlinearity f satisfying a negative feedback condition combined with a boundedness condition. We present a global stability criterion for this family, which in particular unifies the celebrated 3/2-conditions given for the Yorke and the Wright type equations. We illustrate our results with some applications.

Celso Grebogi, ' Stephen M. Hammel, ' ' James A. Yorke, ' and Tim Sauer "'Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 ' 'institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, Maryland 20742 ' 'lvaval Surface Warfare Center, Silter Spring, Maryland 20903-5000 'Department of Mathematical Sciences...

Ditza Auerbach, ' Celso Grebogi, '1 Edward Ott, ' and James A. Yorke ' Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 '2~institute for Physical Sciences and Technology and Department ofMathematics, University of Maryland, College Park, Maryland 20742 t 1Department of Physics and Department of Electrical Engineering, University of Maryland, College Park, Mar...