scholarly journals Euler and RK4 Algorithms Based Implementation of Autonomous Chaotic Generator

2019 ◽  
Vol 8 (6) ◽  
pp. 4161-4165
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Numerical Algorithms ◽  
Vital Role ◽  
Fpga Implementation ◽  
Data Sets ◽  
Key Generation ◽  
Number Generator ◽  
Chaos Generator ◽  
Different Chaotic Systems

Chaotic systems plays a vital role in the field of security, data hiding and steganography. FPGA implementation makes more advantageous compared to analog one. Different chaotic systems like chaos generator and nondeterministic number generator used for security purpose and key generation were successfully realized in FPGA. In this paper, FPGA implementation of Pandey-Baghel-Singh chaotic system (PBSCS) using Euler and RK4 numerical algorithms is presented. Pandey-Baghel-Singh chaotic system were obtained using numerical differential solution and numerically modelled in Verilog with the environment of Xilinx Vivado 2017.3 design suite. The design is verified using experimental setup with the help of interfacing to PC and FPGA family of Artix-7 Nexys 4 DDR and Basys3. Performance of the FPGA based chaotic generator using Euler and RK4 algorithm are analyzed using 1 GB data sets with the maximum operating frequency achieved up to 359.71 MH

scholarly journals Chaos Enhanced Differential Evolution in the Task of Evolutionary Control of Selected Set of Discrete Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Roman Senkerik ◽  
Ivan Zelinka ◽  
Michal Pluhacek ◽  
Donald Davendra ◽  
Zuzana Oplatková Kominkova
Keyword(s):  
Differential Evolution ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Chaotic Map ◽  
Differential Evolution Algorithm ◽  
Pseudorandom Number Generator ◽  
Pseudorandom Sequences ◽  
Evolutionary Technique ◽  
Evolutionary Tuning ◽  
Different Chaotic Systems

Evolutionary technique differential evolution (DE) is used for the evolutionary tuning of controller parameters for the stabilization of set of different chaotic systems. The novelty of the approach is that the selected controlled discrete dissipative chaotic system is used also as the chaotic pseudorandom number generator to drive the mutation and crossover process in the DE. The idea was to utilize the hidden chaotic dynamics in pseudorandom sequences given by chaotic map to help differential evolution algorithm search for the best controller settings for the very same chaotic system. The optimizations were performed for three different chaotic systems, two types of case studies and developed cost functions.

scholarly journals Parallel multi-layer selector S-Box based on lorenz chaotic system with FPGA implementation

2020 ◽  
Vol 19 (2) ◽  
pp. 784
Author(s):  
Mohamed Saber ◽  
Esam Hagras
Keyword(s):  
Power Consumption ◽  
Chaotic System ◽  
High Speed ◽  
Computational Models ◽  
Chaotic Systems ◽  
Fpga Implementation ◽  
Differential Probability ◽  
Substitution Boxes ◽  
Lorenz Chaotic System ◽  
Hidden Data

<p><span>The substitution box (S-Box) is the main block in the encryption system, which replaces the non-encrypted data by dynamic secure and hidden data. S-Box can be designed based on complex nonlinear chaotic systems that presented in recent papers as a chaotic S-Box. The hardware implementation of these chaotic systems suffers from long processing time (low speed), and high-power consumption since it requires a large number of non-linear computational models. In this paper, we present a high-speed FPGA implementation of Parallel Multi-Layer Selector Substitution Boxes based on the Lorenz Chaotic System (PMLS S-Box). The proposed PMLS chaotic S-Box is modeled using Xilinx System Generator (XSG) in 32 bits fixed-point format, and the architecture implemented into Xilinx Spartan-6 X6SLX45 board. The maximum frequency of the proposed PMLS chaotic S-Box is 381.764 MHz, with dissipates of 77 mwatt. Compared to other S-Box chaotic systems, the proposed one achieves a higher frequency and lower power consumption. In addition, the proposed PMLS chaotic S-Box is analyzed based on S-Box standard tests such as; Bijectivity property, nonlinearity, strict avalanche criterion, differential probability, and bits independent criterion. The five different standard results for the proposed S-Box indicate that PMLSC can effectively resist crypto-analysis attacks, and is suitable for secure communications.</span></p>

scholarly journals Transformation of the generalized chaotic system into canonical form

2017 ◽  
Vol 3 (3) ◽  
pp. 117
Author(s):  
Roman Voliansky
Keyword(s):  
Canonical Form ◽  
Chaotic System ◽  
Discrete Model ◽  
Control Algorithm ◽  
Chaotic Systems ◽  
Numerical Algorithms ◽  
Chaotic Attractors ◽  
Output Variable ◽  
State Spaces ◽  
Sample Time

The paper deals with the developing of the numerical algorithms for transformation of generalized chaotic system into canonical form. Such transformation allows us to simplify control algorithm for chaotic system. These algorithms are defined by using Lie derivatives for output variable and solution of nonlinear equations. Usage of proposed algorithm is one of the ways for discovering of new chaotic attractors. These attractors can be obtained by transformation of known chaotic systems into various state spaces. Transformed attractors depend on both parameters of chaotic system and sample time of its discrete model.

scholarly journals FPGA Realization and Lyapunov–Krasovskii Analysis for a Master-Slave Synchronization Scheme Involving Chaotic Systems and Time-Delay Neural Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
J. Perez-Padron ◽  
C. Posadas-Castillo ◽  
J. Paz-Perez ◽  
E. Zambrano-Serrano ◽  
M. A. Platas-Garza
Keyword(s):  
Time Delay ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Tracking Error ◽  
Control Law ◽  
Trajectory Tracking Control ◽  
Field Programmable ◽  
Different Chaotic Systems ◽  
Synchronization Scheme ◽  
Theoretical Results

In this paper, the trajectory tracking control and the field programmable gate array (FPGA) implementation between a recurrent neural network with time delay and a chaotic system are presented. The tracking error is globally asymptotically stabilized by means of a control law generated from the Lyapunov–Krasovskii and Lur’e theory. The applicability of the approach is illustrated by considering two different chaotic systems: Liu chaotic system and Genesio–Tesi chaotic system. The numerical results have shown the effectiveness of obtained theoretical results. Finally, the theoretical results are implemented on an FPGA, confirming the feasibility of the synchronization scheme and showing that it is hardware realizable.

Synchronization of Liu-Su-Liu and Liu-Chen-Liu Chaotic Systems by Nonlinear Feedback Control

2019 ◽  
Vol 16 (12) ◽  
pp. 4903-4907
Author(s):  
Regan Murugesan ◽  
Suresh Rasappan ◽  
Pugalarasu Rajan ◽  
Sathish Kumar Kumaravel
Keyword(s):  
Feedback Control ◽  
Nonlinear Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Control Method ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Nonlinear Control Method ◽  
Different Chaotic Systems

This paper investigates the global chaos synchronization of identical Liu-Su-Liu chaotic systems (2006) and non-identical Liu-Su-Liu chaotic system (2006) and Liu-Chen-Liu chaotic system (2007). In this paper, active nonlinear control method has been successfully applied to synchronize two identical Liu-Su-Liu chaotic systems and then to synchronize two different chaotic systems, viz. Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Since the Lyapunov exponents are not required for these calculations, the active nonlinear control method is effective and convenient to synchronize Liu-Su-Liu and Liu-Chen-Liu chaotic systems. Numerical simulations are also given to illustrate the proposed synchronization approach.

Attack on a Chaos-Based Random Number Generator Using Anticipating Synchronization

2015 ◽  
Vol 25 (02) ◽  
pp. 1550021
Author(s):  
Ramazan Yeniçeri ◽  
Selçuk Kilinç ◽  
Müştak E. Yalçin
Keyword(s):  
Time Delay ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Random Number ◽  
Initial Conditions ◽  
Random Number Generator ◽  
Original System ◽  
Coupled Systems ◽  
Number Generator ◽  
Delay Chaotic System

Chaotic systems have been used in random number generation, owing to the property of sensitive dependence on initial conditions and hence the possibility to produce unpredictable signals. Within the types of chaotic systems, those which are defined by only one delay-differential equation are attractive due to their simple model. On the other hand, it is possible to synchronize to the future states of a time-delay chaotic system by anticipating synchronization. Therefore, random number generator (RNG), which employs such a system, might not be immune to the attacks. In this paper, attack on a chaos-based random number generator using anticipating synchronization is investigated. The considered time-delay chaotic system produces binary signals, which can directly be used as a source of RNG. Anticipating synchronization is obtained by incorporating other systems appropriately coupled to the original one. Quantification of synchronization is given by the bit error between the streams produced by the original and coupled systems. It is shown that the bit streams generated by the original system can be anticipated by the coupled systems beforehand.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

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