Complexity, Risk, and Financial Markets completes a trilogy of books on chaos and fractal analysis. Fractal analysis examines self-similarity or scale invariance, a structure that is often present in seemingly random and otherwise complex processes. Time series, for example, exhibit self-similarity if subsamples resemble compressed versions of longer samples. Pioneered by engineers, mathematici...

A quantum chaos cloning multi-objective evolutionary algorithm was proposed herein based on chaos search ergodicity, quantum computing efficiency and clonal selection theory of antibodies in artificial immune system. The qubits encoded initial population is used in the new algorithm, Chaos quantum rotation gates are introduced to update individuals, crowding distance is used to keep solution po...

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminatin...

Block cipher analysis covers randomness analysis and cryptanalysis. This paper proposes a new method potentially used for randomness analysis and cryptanalysis. The method uses true random sequence concept as a reference for measuring randomness level of a random sequence. By using this concept, this paper defines bias which represents violation of a random sequence from true random sequence. I...

This paper introduces a new chaotic synchronization scheme based on impulsive stability theory. The synchronization of two identical chaotic systems with parametric uncertainties and mismatch is considered. Some sufficient conditions are developed to guarantee the robust synchronization of the chaotic systems. Compared with existing schemes, the amount of information transmitted between the two...

Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. This behavior usually appears in systems that are highly sensitive to initial condition. In these systems, stabilization is a highly considerable tool for eliminating aberrant behaviors. In this paper, the problem of stabilization and tracking the chaos are investigated....

ToToday’s market place is increasingly dynamic and volatile. In this area supply network issues recently have attracted a lot of attention from industrial practitioners and academics worldwide. Chaos theory is the study of complex, nonlinear, dynamic systems. For chaotic systems, a tiny change in conditions may result in an enormous change in system output, whereas substantial changes in condit...

The modern concept of deterministic chaos arises from the mathematical and physical investigation of the topological and dynamical properties of deterministic systems. The notion of deterministic chaos is frequently used in an increasing number of scientific as well as non-scientific contexts, ranging from mathematics and the physics of dynamical systems to all sorts of complicated time evoluti...

In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the concept of disease and the concept of causation. This paper gives a brief introduction to the concepts underlying chaos theory and non-linear dynamics. It is then shown that chaos theory has only very ...