scholarly journals The unified chaotic system describing the Lorenz and Chua systems

2010 ◽  
Vol 23 (3) ◽  
pp. 345-355 ◽  
Author(s):  
Zeraoulia Elhadj ◽  
Clinton Sprott
Keyword(s):  
Chaotic System ◽  
Joint Function ◽  
Unified Chaotic System ◽  
Dynamical Behaviors ◽  
Nonlinear Chaotic System

This paper introduces the dynamical behaviors of a unified nonlinear chaotic system which describes a two-family chaotic system containing the original Lorenz and the original Chua systems as two extremes and some other systems as a transition in between via a new constructed joint function. This system can display two kinds of attractors, those with one scroll and those with two scrolls.

scholarly journals A Novel Method for Constructing the S-Box Based on Spatiotemporal Chaotic Dynamics

2018 ◽  
Vol 8 (12) ◽  
pp. 2650 ◽  
Author(s):  
Liyan Liu ◽  
Yingqian Zhang ◽  
Xingyuan Wang
Keyword(s):  
Performance Analysis ◽  
Chaotic System ◽  
Chaotic Dynamics ◽  
High Dimensional ◽  
Chaotic Sequences ◽  
Dynamical Behaviors ◽  
Nonlinear Chaotic System ◽  
Novel Method ◽  
Spatiotemporal Chaotic System ◽  
Independence Criterion

A novel construction method for a random S-box by using the spatiotemporal nonlinear chaotic system is proposed. The chaotic sequences of the spatiotemporal chaotic system are applied to construct an initial S-box. Then, the permutation operation between independent chaotic sequences is performed to shuffle the elements of the S-box randomly. In comparisons with the former schemes, the results of the performance analysis indicate that the obtained S-box has a better output bit independence criterion and a stronger ability to resist linear password attacks. It also has a high dimensional feature due to the spatiotemporal chaotic dynamical behaviors. The proposed scheme holds superior cryptographic features.

BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM

2002 ◽  
Vol 12 (12) ◽  
pp. 2917-2926 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN ◽  
DAIZHAN CHENG ◽  
SERGEJ CELIKOVSKY
Keyword(s):  
Chaotic System ◽  
System Parameter ◽  
Lorenz System ◽  
Dual Systems ◽  
Chen System ◽  
Entire Spectrum ◽  
Unified Chaotic System ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
New System

This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

A Unified Chaotic System with Various Coexisting Attractors

2021 ◽  
Vol 31 (01) ◽  
pp. 2150013
Author(s):  
Qiang Lai
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Sine Function ◽  
Coexisting Attractors ◽  
Dynamic Behaviors ◽  
Multiple Zeros ◽  
Unified Chaotic System

This article presents a unified four-dimensional autonomous chaotic system with various coexisting attractors. The dynamic behaviors of the system are determined by its special nonlinearities with multiple zeros. Two cases of nonlinearities with sine function of the system are discussed. The symmetrical coexisting attractors, asymmetrical coexisting attractors and infinitely many coexisting attractors in the system are numerically demonstrated. This shows that such a system has an ability to produce abundant coexisting attractors, depending on the number of equilibrium points determined by nonlinearities.

Oyster oscillator: a novel mega-stable nonlinear chaotic system

2021 ◽  
Author(s):  
Balamurali Ramakrishnan ◽  
Atefeh Ahmadi ◽  
Fahimeh Nazarimehr ◽  
Hayder Natiq ◽  
Sajad Jafari ◽  
...  
Keyword(s):  
Chaotic System ◽  
Nonlinear Chaotic System

A NEW CHAOTIC SYSTEM AND ITS GENERATION

2003 ◽  
Vol 13 (01) ◽  
pp. 261-267 ◽  
Author(s):  
WENBO LIU ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Dynamical Behaviors ◽  
New Chaotic System

This Letter introduces a relatively simple three-dimensional continuous autonomous chaotic system, which can display complex 2- and 4-scroll attractors in simulations. Its generation and basic dynamical behaviors are briefly described.

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