scholarly journals Piecewise Linear map enabled Harris Hawk optimization algorithm

2021 ◽  
Vol 1994 (1) ◽  
pp. 012038
Author(s):  
Juan Zhao ◽  
Zheng-Ming Gao ◽  
Yu-Jun Zhang
Keyword(s):  
Optimization Algorithm ◽  
Piecewise Linear ◽  
Linear Map ◽  
Piecewise Linear Map

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

scholarly journals The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions

2015 ◽  
Vol 25 (13) ◽  
pp. 1550184 ◽  
Author(s):  
Carlos Lopesino ◽  
Francisco Balibrea-Iniesta ◽  
Stephen Wiggins ◽  
Ana M. Mancho
Keyword(s):  
Piecewise Linear ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
The Third ◽  
Autonomous Version ◽  
Area Preserving ◽  
Chaotic Saddle

In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley–Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous version and we prove that the first and the third Conley–Moser conditions are satisfied, which imply the existence of a chaotic saddle. Finally, we numerically demonstrate how the structure of this nonautonomous chaotic saddle varies as parameters are varied.

DIGITAL CONTROL AS SOURCE OF CHAOTIC BEHAVIOR

2010 ◽  
Vol 20 (05) ◽  
pp. 1365-1378 ◽  
Author(s):  
GÁBOR CSERNÁK ◽  
GÁBOR STÉPÁN
Keyword(s):  
Mechanical System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Linear Control ◽  
Control Loop ◽  
Digital Implementation ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Chaotic Vibrations ◽  
Processing Delay

In the present paper, we introduce and analyze a mechanical system, in which the digital implementation of a linear control loop may lead to chaotic behavior. The amplitude of such oscillations is usually very small, this is why these are called micro-chaotic vibrations. As a consequence of the digital effects, i.e. the sampling, the processing delay and the round-off error, the behavior of the system can be described by a piecewise linear map, the micro-chaos map. We examine a 2D version of the micro-chaos map and prove that the map is chaotic.

The Dynamics of a Piecewise Linear Map and its Smooth Approximation

1997 ◽  
Vol 07 (02) ◽  
pp. 351-372 ◽  
Author(s):  
D. Aharonov ◽  
R. L. Devaney ◽  
U. Elias
Keyword(s):  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Invariant Curves ◽  
Smooth Approximation ◽  
Linear Map ◽  
Island Structure ◽  
The Real ◽  
Piecewise Linear Map ◽  
Real Analytic ◽  
Area Preserving

The paper describes the dynamics of a piecewise linear area preserving map of the plane, F: (x, y) → (1 - y - |x|, x), as well as that portion of the dynamics that persists when the map is approximated by the real analytic map Fε: (x, y) → (1 - y - fε(x), x), where fε(x) is real analytic and close to |x| for small values of ε. Our goal in this paper is to describe in detail the island structure and the chaotic behavior of the piecewise linear map F. Then we will show that these islands do indeed persist and contain infinitely many invariant curves for Fε, provided that ε is small.

Noise destroys the coexistence of periodic orbits of a piecewise linear map

2013 ◽  
Vol 22 (3) ◽  
pp. 030502 ◽  
Author(s):  
Can-Jun Wang ◽  
Ke-Li Yang ◽  
Shi-Xian Qu
Keyword(s):  
Periodic Orbits ◽  
Piecewise Linear ◽  
Linear Map ◽  
Piecewise Linear Map

Two-Level Secret Key Image Encryption Method Based on Piecewise Linear Map and Logistic Map

2012 ◽  
Vol 241-244 ◽  
pp. 2728-2731
Author(s):  
Yong Zhang
Keyword(s):  
Image Encryption ◽  
Piecewise Linear ◽  
Logistic Map ◽  
Secret Key ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Encryption Schemes ◽  
Secret Keys ◽  
Secret Code ◽  
Encryption Method

Some chaos-based image encryption schemes using plain-images independent secret code streams have weak encryption security and are vulnerable to chosen plaintext and chosen cipher-text attacks. This paper proposed a two-level secret key image encryption method, where the first-level secret key is the private symmetric secret key, and the second-level secret key is derived from both the first-level secret key and the plain image by iterating piecewise linear map and Logistic map. Even though the first-level key is identical, the different plain images will produce different second-level secret keys and different secret code streams. The results show that the proposed has high encryption speed, and also can effectively resist chosen/known plaintext attacks.

Bifurcation Structures in a Bimodal Piecewise Linear Map: Chaotic Dynamics

2015 ◽  
Vol 25 (03) ◽  
pp. 1530006 ◽  
Author(s):  
Anastasiia Panchuk ◽  
Iryna Sushko ◽  
Viktor Avrutin
Keyword(s):  
Parameter Space ◽  
Chaotic Dynamics ◽  
Piecewise Linear ◽  
Chaotic Attractors ◽  
Bifurcation Structure ◽  
Tent Map ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Replacement Technique ◽  
Bifurcation Structures

In this work, we investigate the bifurcation structure of the parameter space of a generic 1D continuous piecewise linear bimodal map focusing on the regions associated with chaotic attractors (cyclic chaotic intervals). The boundaries of these regions corresponding to chaotic attractors with different number of intervals are identified. The results are obtained analytically using the skew tent map and the map replacement technique.

Kendall’s Tau Based Correlation Analysis of Chaotic Sequences Generated by Piecewise Linear Maps

2015 ◽  
Vol 25 (13) ◽  
pp. 1550177
Author(s):  
Zouhair Ben Jemaa ◽  
Daniele Fournier-Prunaret ◽  
Safya Belghith
Keyword(s):  
Correlation Analysis ◽  
Chaotic Maps ◽  
Initial Conditions ◽  
Piecewise Linear ◽  
Chaotic Map ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Chaotic Sequences ◽  
Linear Maps ◽  
Piecewise Linear Maps

In many applications, sequences generated by chaotic maps have been considered as pseudo-random sequences. This paper deals with the correlation between chaotic sequences generated by a given piecewise linear map; we have based the measure of the correlation on the statistics of the Kendall tau, which is usually used in the field of statistics. We considered three piecewise linear maps to generate chaotic sequences and computed the statistics of the Kendall tau of couples of sequences obtained from randomly chosen couples of initial conditions. We essentially found that the results depend on the considered chaotic map and that it is possible to approach the uncorrelated case.

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