A generalized stability theorem for discrete-time nonautonomous chaos system with applications
type: Item
instance of: scholarly article
title: A generalized stability theorem for discrete-time nonautonomous chaos system with applications
zbMATH Open document ID: 1394.39006
DOI: 10.1155/2015/121359
author: Mei Zhang
author: Danling Wang
author: Lequan Min
author: Xue Wang
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: Firstly, this study introduces a definition of generalized stability (GST) in discrete-time nonautonomous chaos system (DNCS), which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG) based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 2. As another application, this study designs a stream avalanche encryption scheme (SAES) in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 6925507
describes a project that uses: NIST Statistical Test Suite
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/121359
OpenAlex ID: W1485771120
Wikidata QID: Q59118440
cites work: Q4217274
cites work: Chaos in Dynamical Systems
cites work: Q4792122
cites work: Q4342896
cites work: Q4676227
cites work: Nonautonomous Beverton-Holt equations and the Cushing-Henson conjectures
cites work: Coherent sets for nonautonomous dynamical systems
cites work: Analysis of a nonautonomous model for migratory birds with saturation incidence rate
cites work: Nonautonomous analysis of steady Korteweg-de Vries waves under nonlocalised forcing
cites work: Synchronization in chaotic systems
cites work: Poly-quadratic stability and global chaos synchronization of discrete time hybrid systems
cites work: Chaos synchronization and parameter identification for gyroscope system
cites work: Synchronization of a chaotic finance system
cites work: Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers
cites work: Sampled-data nonlinear observer design for chaos synchronization: a Lyapunov-based approach
cites work: Generalized synchronization of different dimensional chaotic dynamical systems
cites work: Synchronizing chaotic systems using control based on a special matrix structure and extending to fractional chaotic systems
cites work: Generalized synchronization in linearly coupled time periodic systems
cites work: A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption
cites work: Generalized outer synchronization between complex dynamical networks
cites work: Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications
cites work: Generalized synchronization in an array of nonlinear dynamic systems with applications to chaotic cnn
cites work: Secure communication using a compound signal from generalized synchronizable chaotic systems
cites work: Parameter estimation only from the symbolic sequences generated by chaos system
cites work: Global chaos synchronization of new chaotic systems via nonlinear control
cites work: Lyapunov function, parameter estimation, synchronization and chaotic cryptography
cites work: A novel stream encryption scheme with avalanche effect
description: scientific article; zbMATH DE number 6925507