all areas of physics over the last two decades. Chaos and Complexity in Astrophysics provides a primer on nonlinear dynamics, and gives researchers and graduate students of astrophysics the investigative tools they need to explore chaotic and complex phenomena. Comprehensive mathematical concepts and techniques are introduced at an appropriate level in the first part of the book, before being a...

Introduction: In this paper, a novel complexity measure is proposed to detect dynamical changes in nonlinear systems using ordinal pattern analysis of time series data taken from the system. Epilepsy is considered as a dynamical change in nonlinear and complex brain system. The ability of the proposed measure for characterizing the normal and epileptic EEG signals when the signal is short or is...

Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For period-doubling and band-merging cascades, we derive expressions for the entropy, the interdependence of -mac...

Krylov complexity, or K-complexity for short, has recently emerged as a new probe of chaos in quantum systems. It is measure operator growth space, which conjecturally bounds the measured by out time ordered correlator (OTOC). We study complexity conformal field theories considering arbitrary 2d CFTs, free field, and holographic models. find that bound on OTOC provided reduces to Maldacena, She...

In this paper we propose two cryptographic algorithm AES and RSA Using Chaos. Chaos has attracted much attention in the field of cryptography. It describes a system which is sensitive to initial condition. It generates apparently random behavior but at the same time is completely deterministic Chaos function is used to increase the complexity and Security of the System.AES and RSA are the two c...

In addition to qualitative methods presented in chaos and complexity theories in educational research, this article addresses quantitative methods that may show potential for future research studies. Although much in the social and behavioral sciences literature has focused on computer simulations, this article explores current chaos and complexity methods that have the potential to bridge the ...

We investigate circuit complexity to characterize chaos in multiparticle quantum systems. In the process, we take a stride analyze open systems by using complexity. propose new diagnostic of from based on reduced density matrix exploring different types circuits. Through explicit calculations toy model two coupled harmonic oscillators, where one or both oscillators are inverted, demonstrate tha...