About: Duffing map is a research topic. Over the lifetime, 27 publications have been published within this topic receiving 134 citations.
TL;DR: The study demonstrates that the proposed image encryption algorithm shows advantages of more than 10113 key space and desirable level of security based on the good statistical results and theoretical arguments.
Abstract: We present a novel image encryption algorithm using Chebyshev polynomial based on permutation and substitution and Duffing map based on substitution. Comprehensive security analysis has been performed on the designed scheme using key space analysis, visual testing, histogram analysis, information entropy calculation, correlation coefficient analysis, differential analysis, key sensitivity test, and speed test. The study demonstrates that the proposed image encryption algorithm shows advantages of more than 10(113) key space and desirable level of security based on the good statistical results and theoretical arguments.
TL;DR: Through phase plots, bifurcation diagrams, and Lyapunov exponents, it is shown that the proposed fractional map exhibits a range of different dynamical behaviors including chaos and coexisting attractors.
Abstract: In this paper, we study the dynamics and control of a Caputo fractional difference form of the Duffing map. We use phase plots, bifurcation diagrams, and Lyapunov exponents to establish the existence of chaos over a wide range of fractional orders and examine the nature of the dynamics. Also, we present the 0–1 test to detect chaos and C 0 complexity, which is an alternative nonlinear statistical measure that can quantify the regularity of a time series. In addition, we measure the approximate entropy to see the performance of our numerical results. Through phase plots and bifurcation diagrams, it is shown that the proposed fractional map exhibits a range of different dynamical behaviors including chaos and coexisting attractors. A one-dimensional feedback stabilization controller is proposed. The asymptotic convergence of the proposed controller is established by means of the stability theory of linear fractional order discrete-time systems. Simulation results have been carried out to illustrate the findings of the study.
TL;DR: According to the butterfly effect, modulated Duffing map systems with different initial values by using the microcontroller are implemented and complete the design of large-scale CRNGs and an innovative secure communication system is integrated.
Abstract: This paper is concerned with the design of synchronized large-scale chaos random number generators (CRNGs) and its application to secure communication. In order to increase the diversity of chaotic signals, we firstly introduce additional modulation parameters in the original chaotic Duffing map system to modulate the amplitude and DC offset of the chaotic states. Then according to the butterfly effect, we implement modulated Duffing map systems with different initial values by using the microcontroller and complete the design of large-scale CRNGs. Next, a discrete sliding mode scheme is proposed to solve the synchronization problem of the master-slave large-scale CRNGs. Finally, we integrate the aforementioned results to implement an innovative secure communication system.
TL;DR: In this paper, a two-dimensional diffeomorphism of curvilinear rectangles with transversal homoclinic saddles is proposed to study chaos in dynamical systems.
Abstract: Smale horseshoes, curvilinear rectangles and their U-shaped images patterned on Smale's famous example, provide a rigorous way to study chaos in dynamical systems. The paper is devoted to constructing them in two-dimensional diffeomorphisms with the existence of transversal homoclinic saddles. We first propose an algorithm to automatically construct “horizontal” and “vertical” sides of the curvilinear rectangle near to segments of the stable and of the unstable manifolds, respectively, and then apply it to four classical chaotic maps (the Duffing map, the Henon map, the Ikeda map, and the Lozi map) to verify its effectiveness.
••06 Apr 2017
TL;DR: Simulations results are presented in the paper shows that the encryption algorithm provides encryption speech samples of low residual intelligibility, key sensitivity and high quality recovered signal.
Abstract: This paper presents a private key data encryption algorithm based on three dimensional chaotic map It is based on confusion and diffusion of speech samples using secret keys generated by logistic & two dimensional Duffing map Chaotic systems can generate pseudo random numbers (PRN) of highly complex dynamical properties Three dimensional chaotic functions are proofed with sound randomness and unpredictability In this method, the speech scrambles are compressed by DCT to reduce residual intelligibility In this techniques Speech samples are initially masked by key stream generated by logistic function After first level encryption speech scrambles undergoes permutation process by Duffing map Simulations results are presented in the paper shows that the encryption algorithm provides encryption speech samples of low residual intelligibility, key sensitivity and high quality recovered signal Total key space for the proposed encryption algorithm is (2∧192), which is large enough to protect the information from brute force attack The proposed method is computationally less complex since it uses lower dimensional chaotic maps
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