Evolutionary Algorithm Based Solution of Rössler Chaotic System Using Bernstein Polynomials

2020 ◽  
Vol 17 (7) ◽  
pp. 2932-2939
Author(s):  
Rania A. Alharbey ◽  
Kiran Sultan
Keyword(s):  
Chaotic System ◽  
Fitness Function ◽  
Bernstein Polynomials ◽  
Three Dimensional ◽  
Accurate Estimation ◽  
Interior Point Algorithm ◽  
Research Attention ◽  
Rossler System ◽  
Rössler System ◽  
Error Dynamics

Chaotic systems have gained enormous research attention since the pioneering work of Lorenz. Rössler system stands among the extensively studied classical chaotic models. This paper proposes a technique based on Bernstein Polynomial Basis Function to convert the three-dimensional Rössler system of Ordinary Differential Equations (ODEs) into an error minimization problem. First, the properties of Bernstein Polynomials are applied to derive the fitness function of Rössler chaotic system. Second, in order to obtain the values of unknown Bernstein coefficients to optimize the fitness function, the problem is solved using two versatile algorithms from the family of Evolutionary Algorithms (EAs), Genetic Algorithm (GA) hybridized with Interior Point Algorithm (IPA) and Differential Algorithm (DE). For validity of the proposed technique, simulation results are provided which verify the global stability of error dynamics and provide accurate estimation of the desired parameters.

scholarly journals Generating a New Chaotic System Using Two Chaotic Rossler-Chua Coupling Systems

2021 ◽  
Author(s):  
Ryam Salam Abdulaali ◽  
Raied K. Jamal ◽  
Salam K. Mousa
Keyword(s):  
Time Series ◽  
Dynamic Behavior ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Matlab Program ◽  
Rossler System ◽  
New Chaotic System ◽  
Rössler System ◽  
New System

Abstract It is proposed in this paper that a new chaotic system may be formed by combining two distinct chaotic systems, such as the Rossler system and the Chua system, in which the x dynamic of the Rossler system is linked with the z dynamic of the Chua system, results in a new chaotic system. Some of the basic dynamic behavior is explored and examined for new system by using the Matlab program. They noticed that it was a difference in the time series of the Chua system and this in turn led to a difference in the attractor, as the attractor of the Chua system changed from double scroll to single scroll and this led to change of the bandwidth of the Chua system, meaning that the Rӧssler system affected the Chua system, which led to an increase in the possibility of using this system in secret communications.

On the Ultimate Dynamics of the Four-Dimensional Rössler System

2014 ◽  
Vol 24 (11) ◽  
pp. 1450149 ◽  
Author(s):  
Konstantin E. Starkov
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Invariant Sets ◽  
Limit Sets ◽  
Localization Method ◽  
Dimensional Plane ◽  
Rossler System ◽  
Lasalle Theorem ◽  
Rössler System ◽  
Positive Half

In this paper, we construct the polytope which contains all compact ω-limit sets of the four-dimensional Rössler system which is a generalization of the hyperchaotic Rössler system for the case of positive parameters. Further, we find a few three-dimensional planes containing all compact ω-limit sets for bounded positive half-trajectories located in some subdomains in the half-space z > 0. Besides, we analyze one case in which all compact ω-limit sets in the half-space z > 0 are contained in one three-dimensional plane. Our approach is based on a combination of the LaSalle theorem and the extreme-based localization method of compact invariant sets.

Chaos Synchronization Between Unified Chaotic System And Rossler System

2013 ◽  
Vol 321-324 ◽  
pp. 2464-2470
Author(s):  
Hao Wu ◽  
Bo Lun Xu ◽  
Chang Fan ◽  
Xian Yong Wu
Keyword(s):  
Active Control ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Adaptive Synchronization ◽  
System Parameters ◽  
Unified Chaotic System ◽  
Rossler System ◽  
Response Systems ◽  
Rössler System ◽  
Different Chaotic Systems

In this paper, two synchronization schemes between two different chaotic systems are proposed. Chaos synchronization between unified chaotic system and Rossler system via active control and adaptive control are investigated. Different controllers are designed to synchronize the drive and response systems. Active control synchronization is used when system parameters are known; adaptive synchronization is employed when system parameters are unknown or uncertain. Simulation results show the effectiveness of the proposed schemes.

scholarly journals Differential Transform Method as an Effective Tool for Investigating Fractional Dynamical Systems

2021 ◽  
Vol 11 (15) ◽  
pp. 6955
Author(s):  
Andrzej Rysak ◽  
Magdalena Gregorczyk
Keyword(s):  
Optimal Parameter ◽  
Differential Transform Method ◽  
Bifurcation Diagrams ◽  
Transform Method ◽  
Rossler System ◽  
Differential Transform ◽  
Rössler System ◽  
Fractional System ◽  
Parameter Values

This study investigates the use of the differential transform method (DTM) for integrating the Rössler system of the fractional order. Preliminary studies of the integer-order Rössler system, with reference to other well-established integration methods, made it possible to assess the quality of the method and to determine optimal parameter values that should be used when integrating a system with different dynamic characteristics. Bifurcation diagrams obtained for the Rössler fractional system show that, compared to the RK4 scheme-based integration, the DTM results are more resistant to changes in the fractionality of the system.

Design and optimization of bump (compression surface) for diverterless supersonic inlet

2021 ◽  
pp. 095441002110029
Author(s):  
Irsalan Arif ◽  
Hassan Iftikhar ◽  
Ali Javed
Keyword(s):  
Fitness Function ◽  
Supersonic Jet ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Least Square ◽  
Pressure Recovery ◽  
Design Parameters ◽  
Inlet System ◽  
Design And Optimization ◽  
Supersonic Inlet

In this article design and optimization scheme of a three-dimensional bump surface for a supersonic aircraft is presented. A baseline bump and inlet duct with forward cowl lip is initially modeled in accordance with an existing bump configuration on a supersonic jet aircraft. Various design parameters for bump surface of diverterless supersonic inlet systems are identified, and design space is established using sensitivity analysis to identify the uncertainty associated with each design parameter by the one-factor-at-a-time approach. Subsequently, the designed configurations are selected by performing a three-level design of experiments using the Box–Behnken method and the numerical simulations. Surrogate modeling is carried out by the least square regression method to identify the fitness function, and optimization is performed using genetic algorithm based on pressure recovery as the objective function. The resultant optimized bump configuration demonstrates significant improvement in pressure recovery and flow characteristics as compared to baseline configuration at both supersonic and subsonic flow conditions and at design and off-design conditions. The proposed design and optimization methodology can be applied for optimizing the bump surface design of any diverterless supersonic inlet system for maximizing the intake performance.

Automatic weaving method for three-dimensional composite preforms using vision system

2021 ◽  
pp. 004051752098238
Author(s):  
Siyuan Li ◽  
Zhongde Shan ◽  
Dong Du ◽  
Li Zhan ◽  
Zhikun Li ◽  
...  
Keyword(s):  
Relative Position ◽  
Vision System ◽  
Estimation Error ◽  
Three Dimensional ◽  
Fiber Reinforced Composites ◽  
Accurate Estimation ◽  
Digital Manufacturing ◽  
Relative Rotation ◽  
Reinforced Composites ◽  
Main Structure

Three-dimensional composite preform is the main structure of fiber-reinforced composites. During the weaving process of large-sized three-dimensional composite preform, relative rotation or translation between the fiber feeder and guided array occurs before feeding. Besides, the weaving needles can be at different heights after moving out from the guided array. These problems are mostly detected and adjusted manually. To make the weaving process more precise and efficient, we propose machine vision-based methods which could realize accurate estimation and adjustment of the relative position-pose between the fiber feeder and guided array, and make the needles pressing process automatic by recognizing the position of the weaving needles. The results show that the estimation error of relative position-pose is within 5%, and the rate of unrecognized weaving needles is 2%. Our proposed methods improve the automation level of weaving, and are conducive to the development of preform forming toward digital manufacturing.

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