This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.

You can never step in the same river twice, goes the old adage of philosophy. An observation on the transitory nature of fluids in motion, this saying also describes the endless variations researchers face when studying human movement. Understanding these biodynamics-why the wirewalker doesn't fall-requires a grasp of the constant fluctuations and fine tunings which maintain balance in the complex, fluid system of human locomotion.
Taking a comprehensive approach to the phenomenon of locomotion, Biodynamics: Why the Wirewalker Doesn't Fall integrates physical laws and principles with...

This book concerns the development of a theory of complex phenomena, using such concepts as fractals, chaos, and fractional derivatives; but, most important, the idea of an allometric control process is developed. In summary the theory attempts to explain why the distribution in the intensity of wars is the same as the relative frequency of the number of words used in languages and the number of species evolved over time from one or a few remote ancestors. The theory also describes the similarity in the variability of the number of births to teens in Texas to the number of sexual partners in...

Offers a lens through which modern society is shown to depend on complex networks for its stability. This text reviews, in non-mathematical language, what we know about the development of science in the twenty-first century and how that knowledge influences our world.

One of my favorite quotes is from a letter of Charles Darwin (1887): I have long discovered that geologists never read each other's works, and that the only object in writing a book is proof of earnestness, and that you do not form your opinions without undergoing labour of some kind. It is not clear if this private opinion of Darwin was one that he held to be absolutely true, or was one of those opinions that, as with most of us, coincides with our bad days, but is replaced with a more optimistic view on our good days. I hold the sense of the statement to be true in general, but not with...

This invaluable book captures the proceedings of a workshop that brought together a group of distinguished scientists from a variety of disciplines to discuss how networking influences decision making. The individual lectures interconnect psychological testing, the modeling of neuron networks and brain dynamics to the transport of information within and between complex networks. Of particular importance was the introduction of a new principle that governs how complex networks talk to one another the Principle of Complexity Management (PCM). PCM establishes that the transfer of information...

This exceptional book is concerned with the application of fractals and chaos, as well as other concepts from nonlinear dynamics to biomedical phenomena. Herein we seek to communicate the excitement being experienced by scientists upon making application of these concepts within the life sciences. Mathematical concepts are introduced using biomedical data sets and the phenomena being explained take precedence over the mathematics. In this new edition what has withstood the test of time has been updated and modernized; speculations that were not borne out have been expunged and the...

Networks of Echoes: Imitation, Innovation and Invisible Leaders is a mathematically rigorous and data rich book on a fascinating area of the science and engineering of social webs. There are hundreds of complex network phenomena whose statistical properties are described by inverse power laws. The phenomena of interest are not arcane events that we encounter only fleetingly, but are events that dominate our lives. We examine how this intermittent statistical behavior intertwines itself with what appears to be the organized activity of social groups. The book is structured as answers to...