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Chaos theory has been used for many years in cryptography. In the past few decades, chaos and nonlinear dynamics have been used in the design of hundreds of cryptographic primitives. These algorithms include image encryption algorithms, hash functions, secure pseudo-random number generators, stream ciphers, watermarking, and steganography. [123]
Nonlinear narrative, disjointed narrative, or disrupted narrative is a narrative technique where events are portrayed, for example, out of chronological order or in other ways where the narrative does not follow the direct causality pattern of the events featured, such as parallel distinctive plot lines, dream immersions or narrating another story inside the main plot-line.
A nonlinear dynamical system exhibits chaotic hysteresis if it simultaneously exhibits chaotic dynamics (chaos theory) and hysteresis.As the latter involves the persistence of a state, such as magnetization, after the causal or exogenous force or factor is removed, it involves multiple equilibria for given sets of control conditions.
The Melnikov method is used in many cases to predict the occurrence of chaotic orbits in non-autonomous smooth nonlinear systems under periodic perturbation. According to the method, it is possible to construct a function called the "Melnikov function" which can be used to predict either regular or chaotic behavior of a dynamical system.
Bifurcations and crises in the Ikeda map.. In applied mathematics and astrodynamics, in the theory of dynamical systems, a crisis is the sudden appearance or disappearance of a strange attractor as the parameters of a dynamical system are varied.
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
In this book, Stewart explains chaos theory to an audience presumably unfamiliar with it. As the book progresses the writing changes from simple explanations of chaos theory to in-depth, rigorous mathematical study. Stewart covers mathematical concepts such as differential equations, resonance, nonlinear dynamics, and probability. The book is ...
In mathematics, the normal form of a dynamical system is a simplified form that can be useful in determining the system's behavior.. Normal forms are often used for determining local bifurcations in a system.