scholarly journals Special functions created by Borel-Laplace transform of Hénon map

2011 ◽  
Vol 18 (0) ◽  
pp. 1-11 ◽  
Author(s):  
Koichi Hiraide ◽  
Chihiro Matsuoka
Keyword(s):  
Laplace Transform ◽  
Special Functions ◽  
Hénon Map ◽  
Henon Map

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 The Double Laplace Transform Expressed in terms of the Lerch Transcendent

2021 ◽  
Vol 14 (3) ◽  
pp. 618-637
Author(s):  
Robert Reynolds ◽  
Allan Stauffer
Keyword(s):  
Laplace Transform ◽  
Special Functions ◽  
Fundamental Constants ◽  
Definite Integrals ◽  
Special Values ◽  
Double Laplace Transform ◽  
Lerch Transcendent

In this manuscript, the authors derive a formula for the double Laplace transform expressed in terms of the Lerch Transcendent. The log term mixes the variables so that the integral is not separable except for special values of k. The method of proof follows the method used by us to evaluate single integrals. This transform is then used to derive definite integrals in terms of fundamental constants, elementary and special functions. A summary of the results is produced in the form of a table of definite integrals for easy referencing by readers.

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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