An Efficient Algorithm For Sensitivity Analysis Of Chaotic Systems
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An Efficient Algorithm for Sensitivity Analysis of Chaotic Systems
We propose a transformation of Ruelle's rigorous linear response formula, which is ill-conditioned in its original form, into a well-conditioned ergodic-averaging computation. We prove a decomposition of Ruelle's formula, called the S3 decomposition, that is differentiable on the unstable manifold. The S3 decomposition ensures that one of the resulting terms, the stable contribution, can be computed using a regularized tangent equation, similar to in a non-chaotic system. The remainder, known as the unstable contribution, is regularized and converted into a computable ergodic average. The S3 algorithm presented here can be naturally extended to systems with higher-dimensional unstable manifolds.
Surface Chaos and Its Applications
This book addresses a special topic in the field of nonlinear dynamical systems, develops a new research direction of surface chaos and surface bifurcation. It provides a clear watershed for original nonlinear chaos and bifurcation research. The novel content of this book makes nonlinear system research more systematical and personalized. This book introduces the chaos and bifurcation behavior of surface dynamics in the sense of Li Yorke, the basic properties, Lyapunov exponent and Feigenbaum constant of nonlinear behavior of surface, and obtained the wave behavior of chaotic process in surface motion, the control of surface chaos and bifurcation, and the wide application of surface chaos in engineering technology. Through this book, readers can obtain more abundant and novel contents about surface chaos and surface bifurcation than the existing mixed fitting bifurcation of plane curve and space curve, which can also expand the realm and vision of research.
Cryptanalysis-Driven Chaotic Image Encryption and Its Applications
Author: Heping Wen
language: en
Publisher: Scientific Research Publishing, Inc. USA
Release Date: 2022-12-27
Chaos cryptography is an inter discipline that combines chaotic theory and cryptography, which includes chaotic secure communication system, chaotic symmetric cipher, chaotic public key cipher and chaotic hash function [1]. In this academic monograph, the main object of our discussion is symmetric chaotic cryptography. The block diagram of symmetrical encryption and communication transmission is shown as Figure 1 [2]. The encryption process is ( , ) EK =CP, in which P means plaintext while K means secret key and () E ? represents encryption function. Alice sends the ciphertext which has been encrypted to Bob, the receiving end. Bob makes use of the same secret key which is sent by a secure channel to decrypt and recover the original plaintext ( , ) DK =PC, in which ()D ? is the decryption function. For an attacker Oscar, the ciphertext C is available but the secret key for the secure channel transmission is not known.