We postulate a generalization of well-known logistic map to open the possibility of optimization the modelling process of the population evolution. For proposed generalized equation we illustrate the character of the transition from regularity to chaos for the whole spectrum of model parameters. As an example we consider specific cases for both periodic and chaotic regime. We focus on the chara...

We study the problem of maintaining a (1+2)-factor approximation of the diameter of a stream of points under the sliding window model. In one dimension, we give a simple algorithm that only needs to store O( 1 2 logR) points at any time, where the parameter R denotes the “spread” of the point set. This bound is optimal and improves Feigenbaum, Kannan, and Zhang’s recent solution by two logarith...

Using the nonlinear dissipative kicked oscillator as an example, the correspondence between the descriptions provided by model dynamical systems of different classes is discussed. A detailed study of the approximate 1D map is undertaken: the period doubling is examined and the possibility of non-Feigenbaum period doubling is shown. Illustrations in the form of bifurcation diagrams and sets of i...

Peter Szolovits-Massachusetts Institute of Technology Harry Pople-University of Pittsburgh Casimir A. Kulikowski-Rutgers University Sholom M. Weiss-Rutgers University J. C. Kunz-The Institutes of Medical Science, Pacific Medical Center L. M. Fagan-Stanford University R. J. Fallat-The Institutes of Medical Science, Pacific Medical Center D. H. McClung-The Institutes of Medical Science, Pacific M...

-A new signature-table technique is described together with an improved book-learning procedure which is thought to be much superior to the linear polynomial method. Full use is made of the so-cahed “alpha-beta” pruning and several forms of forward pruning to restrict the spread of the move tree and to permit the program to look ahead to a much greater depth than it otherwise cotdd do. While st...

The field of one-dimensional dynamics, real and complex, emerged from obscurity in the 1970s and has been intensely explored ever since. It combines the depth and complexity of chaotic phenomena with a chance to fully understand it in probabilistic terms: to describe the dynamics of typical orbits for typical maps. It also revealed fascinating universality features that had never been noticed b...

The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a parameter often reveal a complicated intermingling of period-doubling cascades and chaos. Period doubling can be studied at three levels of complexity. The fi...

‘This research was supported by the following grants: NIH Grant RR-00785; NIH Grant RR-00711; Boeing Grant W266875; NASA/Ames Grant NCC 2-274; DARPA Contract N00039-83-C0136; ONR Contract N00014-86-K-0652. We thank Micheal Hewett, M. Vaughan Johnson Jr., Robert Schulman and Jeff Harvey for their work on BBl. We thank Russ Altman, Jim Brinkley, Bruce Duncan, Olivier Lichtarge, John Brugge, and O...