But, surprisingly, one of the most striking and powerful representations of numbers is completely ignored in the mathematics that is taught in schools and it rarely makes an appearance in university courses, unless you take a special option in number theory. Yet continued fractions are one of ...
For these, however, ergodic theory provides new concepts: characteristic exponents, entropy, information dimension, which are reproducibly estimated from physical experiments. The characteristic exponents measure the rate of divergence of nearby trajectories of a dynamical system, the entropy measures the ...
The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involv es the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calc ulations practic al,...
Chaos theory studies the patterns and regularities that arise from disordered systems. It has been applied to many different things, from predicting weather patterns to the stock market. Simply put, chaos theory is an attempt to see and understand the underlying order of complex systems that may ...
In mathematics, a chaos machine is a class of algorithms constructed on the base of chaos theory (mainly deterministic chaos) to producepseudo-random oracle. It was designed specifically to combine the benefits ofhash functionandpseudo-random function. ...
It is so well and carefully written that, despite the complexity of the subject matte and the difficulty of some of the mathematics, virtually everything is completely clear on a first reading. Indeed, the book is much more absorbing than most novels." Probability in the Engineering + ...
It will contribute with reference texts for a broad audience of researchers, practitioners, and advanced students, in this rapidly growing field, which encompasses applied mathematics, experimental biology and medicine, computational biology, biochemistry, physics and computer science. Authors are kindly ...
The way phenomena or processes evolve or change in time is often described by differential equations or difference equations. One of the simplest mathematical situations occurs when the phenomenon can be described by a single number as, for example, when
Chaotic theory has significant potential for improving the performance of metaheuristic algorithms. The integration of chaos-based enhancement within various global optimization algorithms offers significant advantages. Consider, for example, its application within PSO, where it has the potential to deliver ...
Basic theory of fractional differential equations: Second edition 2016, Basic Theory of Fractional Differential Equations: Second Edition Fractional Evolution Equations and Inclusions: Analysis and Control 2016, Fractional Evolution Equations and Inclusions: Analysis and Control Basic theory of fractional differ...