A Useful Chaotic Family with Single Linearity and Circuit Implementation Based on FPGA

2016 ◽  
Vol 26 (01) ◽  
pp. 1750017 ◽  
Author(s):  
Zeshi Yuan ◽  
Hongtao Li ◽  
Xiaohua Zhu
Keyword(s):  
Field Programmable Gate Array ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Register Transfer Level ◽  
Chaotic Circuit ◽  
Chaotic Flows ◽  
Chaotic Model ◽  
Field Programmable ◽  
Simulation Results

Recently, a series of typical three-dimensional dissipative chaotic flows where all but one of the nonlinearities are quadratic are studied. Based on this research, a novel chaotic model with only one single linearity is proposed by introducing cubic terms and four new chaotic systems with various characteristics are found. Besides, a chaotic family with a single linearity is constructed with those four chaotic systems and 12 existing systems SL1–SL[Formula: see text] of the chaotic flows. Exploiting the new systems, basic dynamic behaviors are analyzed, including the strange attractors, equilibrium points, Lyapunov exponents as well as the property of multistability. In addition, the corresponding simulation results are illustrated to show those properties expressly. In realizing the chaotic circuit, we utilize the field programmable gate array (FPGA), which is of considerable flexibility, good programmability and stability, instead of analog devices that are easily affected by surroundings. More importantly, the circuit of the proposed chaotic family is realized on a single FPGA over register transfer level (RTL) using 32-bit fixed-point operation. Finally, an experimental FPGA-based circuit is constructed, and the output results are shown on oscilloscope, which agree well with the numerical simulations.

scholarly journals Mathematical Model and FPGA Realization of a Multi-Stable Chaotic Dynamical System with a Closed Butterfly-Like Curve of Equilibrium Points

2021 ◽  
Vol 11 (2) ◽  
pp. 788
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Talal Bonny ◽  
Sen Zhang ◽  
Sukono ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Field Programmable Gate Array ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Intrinsic Properties ◽  
Chaotic Dynamical System ◽  
Chaotic Model ◽  
Field Programmable ◽  
The Mathematical Model ◽  
New System

This paper starts with a review of three-dimensional chaotic dynamical systems equipped with special curves of balance points. We also propose the mathematical model of a new three-dimensional chaotic system equipped with a closed butterfly-like curve of balance points. By performing a bifurcation study of the new system, we analyze intrinsic properties such as chaoticity, multi-stability, and transient chaos. Finally, we carry out a realization of the new multi-stable chaotic model using Field-Programmable Gate Array (FPGA).

scholarly journals Energy Conservation, Singular Orbits, and FPGA Implementation of Two New Hamiltonian Chaotic Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Enzeng Dong ◽  
Guanghan Liu ◽  
Zenghui Wang ◽  
Zengqiang Chen
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Dynamical Evolution ◽  
Casimir Energy ◽  
Chaotic Attractors ◽  
Chaotic Flows ◽  
Field Programmable ◽  
Singular Orbits ◽  
Nist Tests

Since the conservative chaotic system (CCS) has no general attractors, conservative chaotic flows are more suitable for the chaos-based secure communication than the chaotic attractors. In this paper, two Hamiltonian conservative chaotic systems (HCCSs) are constructed based on the 4D Euler equations and a proposed construction method. These two new systems are investigated by equilibrium points, dynamical evolution map, Hamilton energy, and Casimir energy. They look similar, but it is found that one can be explained using Casimir power and another cannot be explained in terms of the mechanism of chaos. Furthermore, a pseudorandom signal generator is developed based on these proposed systems, which are tested based on NIST tests and implemented by using the field programmable gate array (FPGA) technique.

A New Category of Three-Dimensional Chaotic Flows with Identical Eigenvalues

2020 ◽  
Vol 30 (02) ◽  
pp. 2050026 ◽  
Author(s):  
Zahra Faghani ◽  
Fahimeh Nazarimehr ◽  
Sajad Jafari ◽  
Julien C. Sprott
Keyword(s):  
Chaotic Systems ◽  
Autonomous Systems ◽  
Three Dimensional ◽  
Special Property ◽  
Computer Search ◽  
Chaotic Flows ◽  
Stable Equilibria ◽  
Dynamical Properties ◽  
Simple Systems ◽  
First Time

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems with identical eigenvalues were found. We believe that systems with identical eigenvalues are described here for the first time. These simple systems are listed in this paper, and their dynamical properties are investigated.

scholarly journals A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1931 ◽  
Author(s):  
Sivaperumal Sampath ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee ◽  
Mustafa Mamat ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.

scholarly journals A Multiscroll Chaotic Attractors with Arrangement of Saddle-Shapes and Its Field Programmable Gate Array (FPGA) Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Faqiang Wang ◽  
Yufang Xiao
Keyword(s):  
Chaotic System ◽  
Field Programmable Gate Array ◽  
Equilibrium Points ◽  
Research Result ◽  
Step Function ◽  
Phase Locked Loops ◽  
Chaotic Attractors ◽  
Digital To Analog Converter ◽  
Field Programmable ◽  
Gate Array

Based on the step function and signum function, a chaotic system which can generate multiscroll chaotic attractors with arrangement of saddle-shapes is proposed and the stability of its equilibrium points is analyzed. The under mechanism for the generation of multiscroll chaotic attractors and the reason for the arrangement of saddle shapes and being symmetric about y-axis are presented, and the rule for controlling the number of scroll chaotic attractors with saddle shapes is designed. Based on the core chips including Altera Cyclone IV EP4CE10F17C8 Field Programmable Gate Array and Digital to Analog Converter chip AD9767, the peripheral circuit and the Verilog Hardware Description Language program for realization of the proposed multiscroll chaotic system is constructed and some experimental results are presented for confirmation. The research result shows that the occupation of multipliers and Phase-Locked Loops in Field Programmable Gate Array is zero.

Multiscroll Chaotic Sea Obtained from a Simple 3D System Without Equilibrium

2016 ◽  
Vol 26 (02) ◽  
pp. 1650031 ◽  
Author(s):  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Tomasz Kapitaniak
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Exponents ◽  
Chaotic Systems ◽  
Poincaré Map ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Equilibrium System ◽  
Frequency Spectra ◽  
Chaotic Flows ◽  
New System

Recently, many rare chaotic systems have been found including chaotic systems with no equilibria. However, it is surprising that such a system can exhibit multiscroll chaotic sea. In this paper, a novel no-equilibrium system with multiscroll hidden chaotic sea is introduced. Besides having multiscroll chaotic sea, this system has two more interesting properties. Firstly, it is conservative (which is a rare feature in three-dimensional chaotic flows) but not Hamiltonian. Secondly, it has a coexisting set of nested tori. There is a hidden torus which coexists with the chaotic sea. This new system is investigated through numerical simulations such as phase portraits, Lyapunov exponents, Poincaré map, and frequency spectra. Furthermore, the feasibility of such a system is verified through circuital implementation.

scholarly journals Hardware/software co-design for a parallel three-dimensional bresenham’s algorithm

2019 ◽  
Vol 9 (1) ◽  
pp. 148
Author(s):  
Sarmad Ismael ◽  
Omar Tareq ◽  
Yahya Taher Qassim
Keyword(s):  
Field Programmable Gate Array ◽  
Complete System ◽  
Line Drawing ◽  
Three Dimensional ◽  
End Point ◽  
Field Programmable ◽  
Speed Up ◽  
The One ◽  
Scan Conversion ◽  
Number Of Segments

<p>Line plotting is the one of the basic operations in the scan conversion. Bresenham’s line drawing algorithm is an efficient and high popular algorithm utilized for this purpose. This algorithm starts from one end-point of the line to the other end-point by calculating one point at each step. As a result, the calculation time for all the points depends on the length of the line thereby the number of the total points presented. In this paper, we developed an approach to speed up the Bresenham algorithm by partitioning each line into number of segments, find the points belong to those segments and drawing them simultaneously to formulate the main line. As a result, the higher number of segments generated, the faster the points are calculated. By employing 32 cores in the Field Programmable Gate Array, a line of length 992 points is formulated in 0.31μs only. The complete system is implemented using Zybo board that contains the Xilinx Zynq-7000 chip (Z-7010).<em></em></p>

scholarly journals Author’s reply to: Comments on “Asymptotically stable equilibrium points in new chaotic systems”

Nova Scientia ◽  
2017 ◽  
Vol 9 (19) ◽  
pp. 906-909
Author(s):  
K. Casas-García ◽  
L. A. Quezada-Téllez ◽  
S. Carrillo-Moreno ◽  
J. J. Flores-Godoy ◽  
Guillermo Fernández-Anaya
Keyword(s):  
Dynamic Systems ◽  
Chaotic Systems ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Heteroclinic Orbits ◽  
Stable Equilibrium Point ◽  
Asymptotically Stable ◽  
Linear Quadratic ◽  
The Monte Carlo Method

Since theorem 1 of (Elhadj and Sprott, 2012) is incorrect, some of the systems found in the article (Casas-García et al. 2016) may have homoclinic or heteroclinic orbits and may seem chaos in the Shilnikov sense. However, the fundamental contribution of our paper was to find ten simple, three-dimensional dynamic systems with non-linear quadratic terms that have an asymptotically stable equilibrium point and are chaotic, which was achieved. These were obtained using the Monte Carlo method applied specifically for the search of these systems.

Fabrication Steps and Thermal Modeling of Three-Dimensional Asynchronous Field Programmable Gate Array (3D-AFPGA)

2019 ◽  
Author(s):  
Robert Carroll ◽  
Carlos Gutierrez ◽  
Leila Choobineh ◽  
Robert Geer
Keyword(s):  
Field Programmable Gate Array ◽  
Thermal Modeling ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Temperature Fields ◽  
Junction Temperature ◽  
3D Integration ◽  
Equivalent Thermal Conductivity ◽  
Field Programmable ◽  
Gate Array

Abstract Field Programmable Gate Arrays (FPGA) are integrated circuits (ICs) which can implement virtually any digital function and can be configured by a designer after manufacturing. This is beneficial when dedicated application-specific runs are not time or cost-effective; however, this flexibility comes at the cost of a substantially higher interconnect overhead. Three-dimensional (3D) integration can offer significant improvements in the FPGA architecture by stacking multiple device layers and interconnecting them in the third or vertical dimension, through a substrate, where path lengths are greatly reduced. This will allow for a higher density of devices and improvements in power consumption, signal integrity, and delay. Further, it facilities heterogeneous integration where additional functionalities can be incorporated into the same package as the FPGA, such as sensors, memories, and RF/analog or photonic chips, etc. Traditionally, devices have always been laid out in a planar format. 3D integration is an architecture wherein multiple layers of planar devices are stacked and interconnected using through silicon vias (TSVs) in the vertical direction. This work will specifically detail the development of a processing and fabrication route for a three-dimensional asynchronous field programmable gate array (3D-AFPGA) design based on an extension of preexisting 2D-FPGA tile designs. Since thermal management of 3D-AFPGA is important, numerical simulations performed to predict the temperature distribution and avoid the maximum junction temperature. The numerical thermal modeling for predicting the equivalent thermal conductivity in every layer and three-dimensional temperature fields in the 3D-AFPGA are developed and discussed.

Sign in / Sign up

Export Citation Format

Share Document