Multifractality is ubiquitously observed in complex natural and socioeconomic systems.
Multifractal analysis provides powerful tools to understand the complex nonlinear nature of …

We discuss the concept of discrete-scale invariance and how it leads to complex critical
exponents (or dimensions), ie to the log-periodic corrections to scaling. After their initial …

Concepts, methods and techniques of statistical physics in the study of correlated, as well as
uncorrelated, phenomena are being applied ever increasingly in the natural sciences …

The scientific study of complex systems has transformed a wide range of disciplines in
recent years, enabling researchers in both the natural and social sciences to model and …

This book explains the quantitative reasoning required by the fractional calculus applied to
complex physical, social, and biological phenomena. Fractional calculus is inextricably …

We study a rational expectation model of bubbles and crashes. The model has two
components:(1) our key assumption is that a crash may be caused by local self-reinforcing …

The concept of self-organized criticality was introduced to explain the behaviour of the
sandpile model. In this model, particles are randomly dropped onto a square grid of boxes …

Thirteen years have passed by since the publication of the first edition of this book. Its
favorable reception encouraged us to work on this second edition. We took advantage of this …

This review presents a general theory of financial crashes and of stock market instabilities
that his co-workers and the author have developed over the past seven years. We start by …

In this review article we present some of achievements of econophysics and sociophysics
which appear to us the most significant. We briefly explain what their roles are in building of …