scholarly journals Estimating the Highest Time-Step in Numerical Methods to Enhance the Optimization of Chaotic Oscillators

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1938
Author(s):  
Martín Alejandro Valencia-Ponce  ◽  
Esteban Tlelo-Cuautle ◽  
Luis Gerardo de la Fraga
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Execution Time ◽  
Chaotic Oscillator ◽  
Time Step ◽  
Chaotic Oscillators ◽  
Swarm Optimization ◽  
One Step ◽  
Multi Step Methods

The execution time that takes to perform numerical simulation of a chaotic oscillator mainly depends on the time-step h. This paper shows that the optimization of chaotic oscillators can be enhanced by estimating the highest h in either one-step or multi-step methods. Four chaotic oscillators are used as a case study, and the optimization of their Kaplan-Yorke dimension (DKY) is performed by applying three metaheuristics, namely: particle swarm optimization (PSO), many optimizing liaison (MOL), and differential evolution (DE) algorithms. Three representative one-step and three multi-step methods are used to solve the four chaotic oscillators, for which the estimation of the highest h is obtained from their stability analysis. The optimization results show the effectiveness of using a high h value for the six numerical methods in reducing execution time while maximizing the positive Lyapunov exponent (LE+) and DKY of the chaotic oscillators by applying PSO, MOL, and DE algorithms.

scholarly journals Issues on Applying One- and Multi-Step Numerical Methods to Chaotic Oscillators for FPGA Implementation

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 151
Author(s):  
Omar Guillén-Fernández ◽  
María Fernanda Moreno-López ◽  
Esteban Tlelo-Cuautle
Keyword(s):  
Time Series ◽  
Numerical Methods ◽  
Numerical Method ◽  
Euler Method ◽  
Fpga Implementation ◽  
Chaotic Time Series ◽  
Time Step ◽  
Chaotic Oscillators ◽  
One Step ◽  
Selection Of

Chaotic oscillators have been designed with embedded systems like field-programmable gate arrays (FPGAs), and applied in different engineering areas. However, the majority of works do not detail the issues when choosing a numerical method and the associated electronic implementation. In this manner, we show the FPGA implementation of chaotic and hyper-chaotic oscillators from the selection of a one-step or multi-step numerical method. We highlight that one challenge is the selection of the time-step h to increase the frequency of operation. The case studies include the application of three one-step and three multi-step numerical methods to simulate three chaotic and two hyper-chaotic oscillators. The numerical methods provide similar chaotic time-series, which are used within a time-series analyzer (TISEAN) to evaluate the Lyapunov exponents and Kaplan–Yorke dimension (DKY) of the (hyper-)chaotic oscillators. The oscillators providing higher exponents and DKY are chosen because higher values mean that the chaotic time series may be more random to find applications in chaotic secure communications. In addition, we choose representative numerical methods to perform their FPGA implementation, which hardware resources are described and counted. It is highlighted that the Forward Euler method requires the lowest hardware resources, but it has lower stability and exactness compared to other one-step and multi-step methods.

scholarly journals Optimizing the Kaplan–Yorke Dimension of Chaotic Oscillators Applying DE and PSO

Technologies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 38 ◽  
Author(s):  
Alejandro Silva-Juarez ◽  
Gustavo Rodriguez-Gomez ◽  
Luis Gerardo de la Fraga ◽  
Omar Guillen-Fernandez ◽  
Esteban Tlelo-Cuautle
Keyword(s):  
Mathematical Model ◽  
Time Series ◽  
Color Image ◽  
Equilibrium Points ◽  
Computing Time ◽  
Chaotic Oscillator ◽  
State Variables ◽  
Huge Number ◽  
Chaotic Oscillators ◽  
Swarm Optimization

When a new chaotic oscillator is introduced, it must accomplish characteristics like guaranteeing the existence of a positive Lyapunov exponent and a high Kaplan–Yorke dimension. In some cases, the coefficients of a mathematical model can be varied to increase the values of those characteristics but it is not a trivial task because a very huge number of combinations arise and the required computing time can be unreachable. In this manner, we introduced the optimization of the Kaplan–Yorke dimension of chaotic oscillators by applying metaheuristics, e.g., differential evolution (DE) and particle swarm optimization (PSO) algorithms. We showed the equilibrium points and eigenvalues of three chaotic oscillators that are simulated applying ODE45, and the Kaplan–Yorke dimension was evaluated by Wolf’s method. The chaotic time series of the state variables associated to the highest Kaplan–Yorke dimension provided by DE and PSO are used to encrypt a color image to demonstrate that they are useful in implementing a secure chaotic communication system. Finally, the very low correlation between the chaotic channel and the original color image confirmed the usefulness of optimizing Kaplan–Yorke dimension for cryptographic applications.

scholarly journals Lightweight Blockchain Processing. Case Study: Scanned Document Tracking on Tezos Blockchain

2021 ◽  
Vol 11 (15) ◽  
pp. 7169
Author(s):  
Mohamed Allouche ◽  
Tarek Frikha ◽  
Mihai Mitrea ◽  
Gérard Memmi ◽  
Faten Chaabane
Keyword(s):  
Load Balancing ◽  
Relative Error ◽  
Execution Time ◽  
General Purpose ◽  
Experimental Results ◽  
Raspberry Pi ◽  
Embedded Platform ◽  
Memory Resources ◽  
Processing Solution

To bridge the current gap between the Blockchain expectancies and their intensive computation constraints, the present paper advances a lightweight processing solution, based on a load-balancing architecture, compatible with the lightweight/embedding processing paradigms. In this way, the execution of complex operations is securely delegated to an off-chain general-purpose computing machine while the intimate Blockchain operations are kept on-chain. The illustrations correspond to an on-chain Tezos configuration and to a multiprocessor ARM embedded platform (integrated into a Raspberry Pi). The performances are assessed in terms of security, execution time, and CPU consumption when achieving a visual document fingerprint task. It is thus demonstrated that the advanced solution makes it possible for a computing intensive application to be deployed under severely constrained computation and memory resources, as set by a Raspberry Pi 3. The experimental results show that up to nine Tezos nodes can be deployed on a single Raspberry Pi 3 and that the limitation is not derived from the memory but from the computation resources. The execution time with a limited number of fingerprints is 40% higher than using a classical PC solution (value computed with 95% relative error lower than 5%).

scholarly journals Transient Analysis of Heat Transfer Across the Residential Building Roof with Pcm and Wood Wool- A Case Study by Numerical Simulation Approach

2013 ◽  
Vol 59 (4) ◽  
pp. 483-497 ◽  
Author(s):  
D. Prakash ◽  
P. Ravikumar
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Phase Change ◽  
Phase Change Material ◽  
Transient Analysis ◽  
Residential Building ◽  
Building Roof ◽  
Type 3 ◽  
Change Material

Abstract In this paper, transient analysis on heat transfer across the residential building roof having various materials like wood wool, phase change material and weathering tile is performed by numerical simulation technique. 2-dimensional roof model is created, checked for grid independency and validated with the experimental results. Three different roof structures are included in this study namely roof with (i). Concrete and weathering tile, (ii). Concrete, phase change material and weathering tile and (iii). Concrete, phase change material, wood wool and weathering tile. Roof type 3 restricts 13% of heat entering the room in comparison with roof having only concrete and weathering tile. Also the effect of various roof layers’ thickness in the roof type 3 is investigated and identified that the wood wool plays the major role in arresting the entry of heat in to the room. The average reduction of heat is about 10 % for an increase of a unit thickness of wood wool layer.

scholarly journals Procedure for the Selection of Rubber Compound in Rubber-Metal Springs for Vibration Isolation

Polymers ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1737
Author(s):  
Milan Banić ◽  
Dušan Stamenković ◽  
Aleksandar Miltenović ◽  
Dragan Jovanović ◽  
Milan Tica
Keyword(s):  
Numerical Simulation ◽  
Constitutive Model ◽  
Vibration Isolation ◽  
Correct Selection ◽  
Virtual Experiment ◽  
Rubber Compound ◽  
Key Factor ◽  
Railway Engineering ◽  
Selection Of

The selection of a rubber compound has a determining influence on the final characteristics of rubber-metal springs. Therefore, the correct selection of a rubber compound is a key factor for development of rubber-metal vibration isolation springs with required characteristics. The procedure for the selection of the rubber compound for vibration isolation of rubber-metal springs has been proposed, so that the rubber-metal elements have the necessary characteristics, especially in terms of deflection. The procedure is based on numerical simulation of spring deflection with Bergström-Boyce constitutive model in virtual experiment, with a goal to determine which parameters of the constitutive model will lead to spring required deflection. The procedure was verified by case study defined to select rubber compound for a rubber–metal spring used in railway engineering.

Time suboptimal control of industrial manipulators along specified paths while keeping an end-effector orientation unchanged

Robotica ◽  
2003 ◽  
Vol 21 (2) ◽  
pp. 153-161 ◽  
Author(s):  
S. Kilicaslan ◽  
Y. Ercan
Keyword(s):  
Suboptimal Control ◽  
Time Step ◽  
End Effector ◽  
Industrial Manipulator ◽  
Industrial Manipulators ◽  
Angular Velocities ◽  
System Equations ◽  
Six Degree Of Freedom ◽  
Time Suboptimal Control

A method for the time suboptimal control of an industrial manipulator that moves along a specified path while keeping its end-effector orientation unchanged is proposed. Nonlinear system equations that describe the manipulator motion are linearized at each time step along the path. A method which gives control inputs (joint angular velocities) for time suboptimal control of the manipulator is developed. In the formulation, joint angular velocity and acceleration limitations are also taken into consideration. A six degree of freedom elbow type manipulator is used in a case study to verify the method developed.

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