A novel chaotic attractors in piecewise version of the 3D Henon map

2015 ◽  
Vol 9 ◽  
pp. 461-473
Author(s):  
M. Mammeri
Keyword(s):  
Chaotic Attractors ◽  
Hénon Map ◽  
Henon Map

Relation between Topological Entropies and Fractal Dimensions of Chaotic Attractors of the Hénon Map

2012 ◽  
Vol 569 ◽  
pp. 447-450
Author(s):  
Xiao Zhou Chen ◽  
Liang Lin Xiong ◽  
Long Li
Keyword(s):  
Linear Relation ◽  
Chaotic Dynamics ◽  
Fractal Dimensions ◽  
Chaotic Attractors ◽  
Two Dimensional ◽  
Hénon Map ◽  
Henon Map ◽  
Efficient Approach ◽  
Integral Relationship

In two-dimensional chaotic dynamics, relationship between fractal dimensions and topological entropies is an important issue to understand the chaotic attractors of Hénon map. we proposed a efficient approach for the estimation of topological entropies through the study on the integral relationship between fractal dimensions and topological entropies. Our result found that there is an approximate linear relation between their topological entropies and fractal dimensions.

scholarly journals Complex Dynamics in Generalized Hénon Map

2015 ◽  
Vol 2015 ◽  
pp. 1-18
Author(s):  
Meixiang Cai
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Complex Dynamics ◽  
Chaotic Attractors ◽  
Jacobian Determinant ◽  
Flip Bifurcation ◽  
Hénon Map ◽  
Henon Map ◽  
Fold Bifurcation ◽  
Generalized Hénon Map

The complex dynamics of generalized Hénon map with nonconstant Jacobian determinant are investigated. The conditions of existence for fold bifurcation, flip bifurcation, and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory and checked up by numerical simulations. Chaos in the sense of Marotto's definition is proved by analytical and numerical methods. The numerical simulations show the consistence with the theoretical analysis and reveal some new complex phenomena which can not be given by theoretical analysis, such as the invariant cycles which are irregular closed graphics, the six and forty-one coexisting invariant cycles, and the two, six, seven, nine, ten, and thirteen coexisting chaotic attractors, and some kinds of strange chaotic attractors.

Autoregressive self-tuning feedback control of the Hénon map

1996 ◽  
Vol 54 (6) ◽  
pp. 6201-6206 ◽  
Author(s):  
Michael E. Brandt ◽  
Ahmet Ademoǧlu ◽  
Dejian Lai ◽  
Guanrong Chen
Keyword(s):  
Feedback Control ◽  
Hénon Map ◽  
Henon Map ◽  
Self Tuning

scholarly journals Detecting and stabilizing periodic orbits of chaotic Henon map through predictive control

2018 ◽  
Vol 27 (2018) ◽  
pp. 73-78
Author(s):  
Dumitru Deleanu
Keyword(s):  
Periodic Orbits ◽  
Predictive Control ◽  
Nonnegative Integer ◽  
Strange Attractor ◽  
Discrete System ◽  
Control Method ◽  
Nonlinear Mapping ◽  
Unstable Periodic Orbits ◽  
Hénon Map ◽  
Henon Map

The predictive control method is one of the proposed techniques based on the location and stabilization of the unstable periodic orbits (UPOs) embedded in the strange attractor of a nonlinear mapping. It assumes the addition of a small control term to the uncontrolled state of the discrete system. This term depends on the predictive state ps + 1 and p(s + 1) + 1 iterations forward, where s is the length of the UPO, and p is a large enough nonnegative integer. In this paper, extensive numerical simulations on the Henon map are carried out to confirm the ability of the predictive control to detect and stabilize all the UPOs up to a maximum length of the period. The role played by each involved parameter is investigated and additional results to those reported in the literature are presented.

scholarly journals Key Generation based on Henon map and Lorenz system

2020 ◽  
Vol 31 (1) ◽  
pp. 41
Author(s):  
Ansam Sabah Bader ◽  
Shaymaa Hameed ◽  
Maisa’a Abid Ali K.
Keyword(s):  
Lorenz System ◽  
New Method ◽  
Key Generation ◽  
Hénon Map ◽  
Henon Map ◽  
Data Authentication ◽  
Secure Information ◽  
Data Store ◽  
Significant Process ◽  
Encryption Algorithms

Securing information has been the most significant process for communication and data store. Orderly to secure information such as data authentication,  data integrity, and confidentiality must be verified based on algorithms of cryptography. Where, the most important part of any encryption algorithms is the key which specifies if the system is strong enough or not. The proposal of this paper is a new method to generate keys based on two kinds of chaos theory in order to improve the security of cryptographic algorithms. The base of this proposal is to investigate a new method for generating random numbers by using the 3D Lorenz system and 2D Henon map. The newly generated keys have successfully passed the National Institute of Standards and Technology (NIST) statistical test suite

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