Reality of Chaos in the Hénon Mapping

Lozi Mappings ◽  
2013 ◽  
pp. 26-66
Keyword(s):  
Henon Mapping

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

Structure of the attracting set of a piecewise linear Hénon mapping

1988 ◽  
Vol 9 (9) ◽  
pp. 827-836
Author(s):  
Zhu Zhao-xuan ◽  
Liu Zeng-rong
Keyword(s):  
Piecewise Linear ◽  
Attracting Set ◽  
Henon Mapping

Displacement Analysis of the 4SPS-2CCS Mechanism Based on Hyper-Chaotic Newton-Downhill Method

2011 ◽  
Vol 230-232 ◽  
pp. 733-737
Author(s):  
You Xin Luo ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Parallel Robot ◽  
Number Range ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Henon Mapping ◽  
Solutions Of Equations

The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of Newton-downhill method, we can find all the solutions of equations quickly. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 4SPS-2CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic Newton-downhill method finding solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

scholarly journals Reversible Data Hiding in a Chaotic Encryption Domain Based on Odevity Verification

2021 ◽  
Vol 13 (6) ◽  
pp. 1-14
Author(s):  
Lianshan Liu ◽  
Xiaoli Wang ◽  
Lingzhuang Meng ◽  
Gang Tian ◽  
Ting Wang
Keyword(s):  
Data Hiding ◽  
Reversible Data Hiding ◽  
Signal To Noise Ratio ◽  
Chaotic Encryption ◽  
Original Image ◽  
Embedding Capacity ◽  
Logistic Mapping ◽  
Henon Mapping ◽  
Pixel Value ◽  
Carrier Image

On the premise of guaranteeing the visual effect, in order to improve the security of the image containing digital watermarking and restore the carrier image without distortion, reversible data hiding in chaotic encryption domain based on odevity verification was proposed. The original image was scrambled and encrypted by Henon mapping, and the redundancy between the pixels of the encrypted image was lost. Then, the embedding capacity of watermarking can be improved by using odevity verification, and the embedding location of watermarking can be randomly selected by using logistic mapping. When extracting the watermarking, the embedded data was judged according to the odevity of the pixel value of the embedding position of the watermarking, and the carrier image was restored nondestructively by odevity check image. The experimental results show that the peak signal-to-noise ratio (PSNR) of the original image is above 53 decibels after the image is decrypted and restored after embedding the watermarking in the encrypted domain, and the invisibility is good.

scholarly journals Shift Automorphisms in the Hénon Mapping

2020 ◽  
pp. 555-565
Author(s):  
R. Devaney ◽  
Z. Nitecki
Keyword(s):  
Henon Mapping

scholarly journals A Color Image Encryption Scheme Based on a Novel 3D Chaotic Mapping

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Chunyuan Liu ◽  
Qun Ding
Keyword(s):  
Image Encryption ◽  
Color Image ◽  
Security Analysis ◽  
Superior Performance ◽  
Secret Key ◽  
Color Image Encryption ◽  
Chaotic Mapping ◽  
Cryptographic Algorithm ◽  
Henon Mapping ◽  
Low Dimensional

Low-dimensional chaotic mappings are simple functions that have low computation cost and are easy to realize, but applying them in a cryptographic algorithm will lead to security vulnerabilities. To overcome this shortcoming, this paper proposes the coupled chaotic system, which coupled the piecewise and Henon mapping. Simulation results indicate that the novel mapping has better complexity and initial sensitivity and larger key space compared with the original mapping. Then, a new color image encryption algorithm is proposed based on the new chaotic mapping. The algorithm has two processes: diffusion and confusion. In this scheme, the key is more than 2 216 , and SSIM and PSNR are 0.009675 and 8.6767, respectively. The secret key is applied in the shuffling and diffusion. Security analysis indicates that the proposed scheme can resist cryptanalytic attacks. It has superior performance and has high security.

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