Since Li and Yorke first gave the definition of chaos by using strict mathematical language in 1975 [1], the research on chaos has greatly influenced modern science, not just natural sciences but also several social sciences, such as economics, sociology, and philosophy. The theory of chaos convinced scientists that a simple definite system can produce complicated features and a complex system ...

A brief review of the manifestations of classical chaos observed in atomic systems is presented. Particular attention is paid to the analysis of atomic spectra by periodic orbit-type theories. For diamagnetic non-hydrogenic Rydberg atoms, the dynamical explanation for observed spectral features has been disputed. By building on our previous work on the photoabsorption spectrum, we show how, by ...

We show that the so-called chaos bound, proposed by Maldacena, Shenker & Stanford, can be violated in f(T) teleparallel gravity. In particular, it is possible to select a new gravitational Lyapunov parameter, controlling chaotization of circular trajectories, black hole photo-sphere, exceed Stanford thermal bound. This feature alters standard quasi-normal modes and ringdown phase after merging ...

Chaos optimization algorithm (COA), which has the features of easy implementation, short execution time and robust mechanisms of escaping from the local optimum, is a promising tool for the engineering applications. The design of approaches to improve the convergence of the COA is a challenging issue. Improved mutative-scale parallel chaotic optimization algorithm (MPCOA) are proposed in this p...

The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here I review a variety of invariant measures for quantifying chaotic dynamics in relativity that exploit the coordinate independence of fractal dimensions and symbolic entropies. 1 Time and chaos Historically, chaos theory was developed for Newtonian dynamics where time and spac...

We investigate chaotic behavior of ordinary differential equations with a homoclinic orbit to a dissipative saddle point under a general time dependent forcing without any periodicity in time. We study Poincaré return maps in extended phase space, introducing a characteristic function that generalizes the classic Melnikov function. We then show that the dynamics of the solutions of these equati...

Walking, as an important transportation mode, plays a large part in urban transportation systems. This mode is of great importance for planners and decision-makers because of its impact on environmental and health aspects of communities. However, this mode is so complex in nature that makes it difficult to study or model. On the other hand, chaos theory studies complex dynamical nonlinear syste...

Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...