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At least 1,243 records · Page 69Linked to original sources
PubMed2001

Mandelbrot set in coupled logistic maps and in an electronic experiment.

We suggest an approach to constructing physical systems with dynamical characteristics of the complex analytic iterative maps. The idea follows from a simple notion that the complex quadratic map by a variable change may be transformed into a set of two identical real one-dimensional quadratic maps with a particular coupling. Hence, dynamical behavior of similar nature may occur in coupled dissipative nonlinear systems, which relate to the Feigenbaum universality class. To substantiate the feasibility of this concept, we consider an electronic system, which exhibits dynamical phenomena intrinsic to complex analytic maps. Experimental results are presented, providing the Mandelbrot set in the parameter plane of this physical system.

Journal Article↗
PubMed2002

Nonequilibrium probabilistic dynamics of the logistic map at the edge of chaos.

We consider nonequilibrium probabilistic dynamics in logisticlike maps x(t+1)=1-a|x(t)|(z), (z>1) at their chaos threshold: We first introduce many initial conditions within one among W>>1 intervals partitioning the phase space and focus on the unique value q(sen)<1 for which the entropic form S(q) identical with (1- summation operator Wp(q)(i))/(q-1) linearly increases with time. We then verify that S(q(sen))(t)-S(q(sen))( infinity ) vanishes like t(-1/[q(rel)(W)-1]) [q(rel)(W)>1]. We finally exhibit a new finite-size scaling, q(rel)( infinity )-q(rel)(W) proportional, variant W(-|q(sen)|). This establishes quantitatively, for the first time, a long pursued relation between sensitivity to the initial conditions and relaxation, concepts which play central roles in nonextensive statistical mechanics.

Journal Article↗
PubMed1982

Logistics and management of clinical trials.

This chapter is concerned with some of the more mundane aspects of the day to day design, planning, documentation, and management of clinical trials, rather than with the finer points of trial design which are dealt with in detail elsewhere. The points considered here, taken individually, seem obvious and trivial but it is hoped that some may be helpful in obtaining the maximum return for the work invested in running a trial.

Clinical Trials as Topic↗