Mechanics Analysis and Hardware Implementation of a New 3D Chaotic System

2018 ◽  
Vol 28 (13) ◽  
pp. 1850161 ◽  
Author(s):  
Hongyan Jia ◽  
Zhiqiang Guo ◽  
Shanfeng Wang ◽  
Zengqiang Chen
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Type System ◽  
Type Systems ◽  
Physical Models ◽  
Key Factors ◽  
Kolmogorov Type ◽  
Inertial Torque ◽  
Field Programmable ◽  
Physical Background

In this study, a new 3D chaotic system was first transformed into a Kolmogorov-type system to describe the vector field from the viewpoint of torque. In this Kolmogorov-type system, only inertial torque and non-Rayleigh dissipation exist. Thus, this is different from previously reported Kolmogorov-type systems that are generally decomposed into inertial torque, internal torque, dissipation, and external torque. Moreover, by analyzing these two torques, the physical background of the system and the key factors of chaos generation were also determined. That is, the inertial torque and non-Rayleigh dissipation are responsible for chaos generation in the new 3D chaotic system. Then, the Casimir function and Hamiltonian energy function were also analyzed to investigate the cycling of energy in the chaotic system. Finally, both an analog circuit and a Field Programmable Gate Array (FPGA) circuit were designed to implement the chaotic system. All of the experimentally obtained results are consistent with the results of numerical analysis, which did not only indicate the chaotic characteristics of the 3D chaotic system physically, but also provided physical models for engineering applications.

Force Analysis of Qi Chaotic System

2016 ◽  
Vol 26 (14) ◽  
pp. 1650237 ◽  
Author(s):  
Guoyuan Qi ◽  
Xiyin Liang
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Casimir Energy ◽  
State Variables ◽  
Force Analysis ◽  
Key Factors ◽  
Kolmogorov Type ◽  
Different Types ◽  
Inertial Torque ◽  
Energy Law

The Qi chaotic system is transformed into Kolmogorov type of system. The vector field of the Qi chaotic system is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. Angular momentum representing the physical analogue of the state variables of the chaotic system is identified. The Casimir energy law relating to the orbital behavior is identified and the bound of Qi chaotic attractor is given. Five cases of study have been conducted to discover the insights and functions of different types of torques of the chaotic attractor and also the key factors of producing different types of modes of dynamics.

Mechanism and Energy Cycling of the Qi Four-Wing Chaotic System

2017 ◽  
Vol 27 (12) ◽  
pp. 1750180 ◽  
Author(s):  
Guoyuan Qi ◽  
Xiyin Liang
Keyword(s):  
Angular Momentum ◽  
Chaotic System ◽  
Common Ground ◽  
Type System ◽  
Casimir Function ◽  
State Variables ◽  
Key Factors ◽  
External Energy ◽  
Kolmogorov Type ◽  
Extremal Points

The Qi four-wing chaotic system is transformed into a Kolmogorov-type system, thereby building a bridge between a numerical chaotic system and a physical chaotic system that is convenient for analysis when finding common ground between the two. The vector field is decomposed into four types of torques: inertial, internal, dissipative and external. The angular momentum representing the physical analogue of the state variables of the chaotic system is identified. The cycling of energy among potential energy, kinetic energy, dissipation, and external energy is analyzed. The Casimir function is employed to identify the key factors producing chaos and other dynamical modes. The system is non-Rayleigh dissipative, which determines the extremal points of Casimir function to form a hyperboloid instead of ellipsoid.

scholarly journals A Novel Chaotic System with Two Circles of Equilibrium Points: Multistability, Electronic Circuit and FPGA Realization

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1211 ◽  
Author(s):  
Sambas ◽  
Vaidyanathan ◽  
Tlelo-Cuautle ◽  
Zhang ◽  
Sukono ◽  
...  
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Digital Implementation ◽  
Gate Arrays ◽  
New Chaotic System ◽  
Field Programmable ◽  
Programmable Gate Arrays ◽  
Good Agreement

This paper introduces a new chaotic system with two circles of equilibrium points. The dynamical properties of the proposed dynamical system are investigated through evaluating Lyapunov exponents, bifurcation diagram and multistability. The qualitative study shows that the new system exhibits coexisting periodic and chaotic attractors for different values of parameters. The new chaotic system is implemented in both analog and digital electronics. In the former case, we introduce the analog circuit of the proposed chaotic system with two circles of equilibrium points using amplifiers, which is simulated in MultiSIM software, version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB. In addition, we perform the digital implementation of the new chaotic system using field-programmable gate arrays (FPGA), the experimental observations of the attractors of which confirm its suitability to generate chaotic behavior.

Dynamical Mechanism and Energy Conversion of the Couette–Taylor Flow

2019 ◽  
Vol 29 (08) ◽  
pp. 1950100
Author(s):  
Heyuan Wang
Keyword(s):  
Reynolds Number ◽  
Energy Conversion ◽  
Physical Interpretation ◽  
Type System ◽  
Casimir Function ◽  
Key Factors ◽  
Kolmogorov Type ◽  
Dynamical Mechanism ◽  
Taylor Flow ◽  
Kinetic And Potential Energies

In this paper, we study the dynamical mechanism and energy conversion of the Couette–Taylor flow. The Couette–Taylor flow chaotic system is transformed into the Kolmogorov type system, which is decomposed into four types of torques. Combining different torques, the key factors of chaos generation and the physical interpretation of the Couette–Taylor flow are studied. We further investigate the conversion among Hamiltonian, kinetic and potential energies, as well as the correlation between the energies and the Reynolds number. It is concluded that the combination of the four torques is necessary to produce chaos, and the system can produce chaos only when the dissipative torques match the driving (external) torques. Any combination of three types of torques cannot produce chaos. Moreover, we introduce the Casimir function to analyze the system dynamics, and choose its derivation to formulate the energy conversion. The bound of chaotic attractor is obtained by the Casimir function and Lagrange multiplier. It is found that the Casimir function reflects the energy conversion and the distance between the orbit and the equilibria.

scholarly journals Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 678 ◽  
Author(s):  
Yixuan Song ◽  
Fang Yuan ◽  
Yuxia Li
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Random Sequence ◽  
Mathematical Expression ◽  
Digital Signal ◽  
Approximate Entropy ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Key Space ◽  
Sequence Generator

In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.

A system of constructor classes: overloading and implicit higher-order polymorphism

1995 ◽  
Vol 5 (1) ◽  
pp. 1-35 ◽  
Author(s):  
Mark P. Jones
Keyword(s):  
Type System ◽  
Type Systems ◽  
Natural Generalization ◽  
Higher Order ◽  
Functional Language ◽  
Effective Algorithm ◽  
Prototype Implementation ◽  
Type Classes

AbstractThis paper describes a flexible type system that combines overloading and higher-order polymorphism in an implicitly typed language using a system of constructor classes—a natural generalization of type classes in Haskell. We present a range of examples to demonstrate the usefulness of such a system. In particular, we show how constructor classes can be used to support the use of monads in a functional language. The underlying type system permits higher-order polymorphism but retains many of the attractive features that have made Hindley/Milner type systems so popular. In particular, there is an effective algorithm that can be used to calculate principal types without the need for explicit type or kind annotations. A prototype implementation has been developed providing, amongst other things, the first concrete implementation of monad comprehensions known to us at the time of writing.

scholarly journals Automating Proof Steps of Progress Proofs: Comparing Vampire and Dafny

10.29007/5zjp ◽  
2018 ◽  
Author(s):  
Sylvia Grewe ◽  
Sebastian Erdweg ◽  
Mira Mezini
Keyword(s):  
Formal Methods ◽  
Programming Language ◽  
Type System ◽  
Type Systems ◽  
Domain Specific Languages ◽  
Smt Solver ◽  
Domain Specific ◽  
Efficient Type

\noindent Developing provably sound type systems is a non-trivial task which, as of today, typically requires expert skills in formal methods and a considerable amount of time. Our Veritas~\cite{GreweErdwegWittmannMezini15} project aims at providing support for the development of soundness proofs of type systems and efficient type checker implementations from specifications of type systems. To this end, we investigate how to best automate typical steps within type soundness proofs.\noindent In this paper, we focus on progress proofs for type systems of domain-specific languages. As a running example for such a type system, we model a subset SQL and augment it with a type system. We compare two different approaches for automating proof steps of the progress proofs for this type system against each other: firstly, our own tool Veritas, which translates proof goals and specifications automatically to TPTP~\cite{Sutcliffe98} and calls Vampire~\cite{KovacsV13} on them, and secondly, the programming language Dafny~\cite{Leino2010}, which translates proof goals and specifications to the intermediate verification language Boogie 2~\cite{Leino2008} and calls the SMT solver Z3~\cite{DeMoura2008} on them. We find that Vampire and Dafny are equally well-suited for automatically proving simple steps within progress proofs.

scholarly journals Laser Doppler Flowmetry versatile acquisition system with low quantization error

2018 ◽  
Vol 4 (1) ◽  
pp. 25
Author(s):  
Francesco Marrazzi ◽  
Frederic Truffer ◽  
Martial Geiser
Keyword(s):  
Laser Doppler Flowmetry ◽  
Analog Circuit ◽  
Scattered Light ◽  
Blood Perfusion ◽  
Electrical Signal ◽  
Laser Doppler ◽  
Physical Models ◽  
Acquisition System ◽  
Invasive Technique ◽  
Doppler Flowmetry

The Laser Doppler Flowmetry (LDF) is a non-invasive technique used to evaluate blood perfusion of various human tissues like the skin or the fundus of the eye. It is based on the scattering of light on moving red blood cells in tissue. Frequency shifted scattered light is detected and provide an electrical signal. Physical models for LDF use the DC and AC components of this signal. If AC is small relative to the DC, digitalization becomes an issue, and if more than two LDF signal acquisitions and analysis have to be done simultaneously, the device becomes expensive and bulky. We propose here a versatile and inexpensive acquisition system, which overcomes quantization errors issue by first separating DC from AC, then amplifying AC and finally recombining both signals before digitalization. We designed an analog circuit combined with a 12 bit analog-to-digital converter, a microcontroller unit and a Raspberry Pi2 (Rpi2) for the signal processing. Results are accessed remotely from the Rpi2 through HTTP protocol. Multiple systems can easily be used simultaneously for multichannel acquisitions.

How to evaluate the performance of gradual type systems

2019 ◽  
Vol 29 ◽  
Author(s):  
BEN GREENMAN ◽  
ASUMU TAKIKAWA ◽  
MAX S. NEW ◽  
DANIEL FELTEY ◽  
ROBERT BRUCE FINDLER ◽  
...  
Keyword(s):  
Type System ◽  
Type Systems ◽  
Relative Performance ◽  
Systematic Evaluation ◽  
Gradual Typing ◽  
The Absolute

Abstract A sound gradual type system ensures that untyped components of a program can never break the guarantees of statically typed components. This assurance relies on runtime checks, which in turn impose performance overhead in proportion to the frequency and nature of interaction between typed and untyped components. The literature on gradual typing lacks rigorous descriptions of methods for measuring the performance of gradual type systems. This gap has consequences for the implementors of gradual type systems and developers who use such systems. Without systematic evaluation of mixed-typed programs, implementors cannot precisely determine how improvements to a gradual type system affect performance. Developers cannot predict whether adding types to part of a program will significantly degrade (or improve) its performance. This paper presents the first method for evaluating the performance of sound gradual type systems. The method quantifies both the absolute performance of a gradual type system and the relative performance of two implementations of the same gradual type system. To validate the method, the paper reports on its application to 20 programs and 3 implementations of Typed Racket.

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