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.

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 and Energy Operation of Chaotic System of Permanent-Magnet Synchronous Motor

2017 ◽  
Vol 27 (14) ◽  
pp. 1750216 ◽  
Author(s):  
Guoyuan Qi ◽  
Jianbing Hu
Keyword(s):  
Permanent Magnet ◽  
Permanent Magnet Synchronous Motor ◽  
Pitchfork Bifurcation ◽  
Synchronous Motor ◽  
Casimir Energy ◽  
Rate Of Change ◽  
Dynamic Force ◽  
Force Analysis ◽  
Different Types ◽  
Motor Error

The disadvantage of a nondimensionalized model of a permanent-magnet synchronous Motor (PMSM) is identified. The original PMSM model is transformed into a Kolmogorov system to aid dynamic force analysis. The vector field of the PMSM is analogous to the force field including four types of torque — inertial, internal, dissipative, and generalized external. Using the feedback thought, the error torque between external torque and dissipative torque is identified. The pitchfork bifurcation of the PMSM is performed. Four forms of energy are identified for the system — kinetic, potential, dissipative, and supplied. The physical interpretations of the decomposition of force and energy exchange are given. Casimir energy is stored energy, and its rate of change is the error power between the dissipative energy and the energy supplied to the motor. Error torque and error power influence the different types of dynamic modes. The Hamiltonian energy and Casimir energy are compared to find the function of each in producing the dynamic modes. A supremum bound for the chaotic attractor is proposed using the error power and Lagrange multiplier.

Constructing a Class of Four-Dimensional Correlative and Switchable Hyperchaotic Systems

2010 ◽  
Vol 44-47 ◽  
pp. 1802-1806
Author(s):  
Fan Yang ◽  
Dong Li ◽  
Hong Qing Tu
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Nonlinear Functions ◽  
Basic Properties ◽  
Hyperchaotic Systems

A class of four-dimensional correlative and switchable hyperchaotic systems were built by adding state variables, nonlinear functions or using the method of anti-control the three-dimensional chaotic system. We studied detailedly some of its basic properties, such as the feature of equilibrium, the phase portraits of hyper chaotic attractor, Lyapunov exponent and the evolutive course of systemic dynamical action.

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.

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

scholarly journals A New Design of Sydney’s Frontport Check-in System

2021 ◽  
Vol 13 (7) ◽  
pp. 3850
Author(s):  
Ting Liu ◽  
Gabriel Lodewijks
Keyword(s):  
Swot Analysis ◽  
Control Measures ◽  
Key Factors ◽  
Scheme Design ◽  
Different Types ◽  
Baggage Handling ◽  
Loading And Unloading ◽  
The Cost ◽  
Main Engine ◽  
Process Method

This paper proposed a scheme design for Sydney’s frontport check-in system, which completes check-in and baggage drop-off at Sydney’s Circular Quay, and transports the baggage to Sydney Kingsford Smith Airport by waterway, and provided a strengths, weaknesses, opportunities and threats (SWOT) analysis of Sydney’s frontport check-in system. Using the process method of quality management, the frontport check-in process was divided into three sub-processes: baggage consignment, baggage packing and transportation, and airport baggage handling. The eight key elements of each sub-process such as input, output, resources, and methods, etc. were discussed, the key factors influencing the cost of baggage transportation were analyzed, and the cost control measures such as adopting economic speed, reducing fuel consumption of the main engine, improving the ship loading rate, and raising loading and unloading efficiency were proposed. At the same time, two different types of baggage transportation ships and other parameters that affect the cost such as the number of berths, ships, lifting machineries, and the yard area were analyzed and calculated through calculation cases. This scheme is a beneficial addition to the existing in-town check-in system.

The combination of different open innovations: a longitudinal case study

2019 ◽  
Vol 13 (2) ◽  
pp. 342-362
Author(s):  
Xiaodong Yuan ◽  
Xiaotao Li
Keyword(s):  
New Product Development ◽  
Open Innovation ◽  
Point Of View ◽  
Longitudinal Case Study ◽  
Key Factors ◽  
Content Type ◽  
Strategic Direction ◽  
Different Types ◽  
Innovation Capacity

Purpose The purpose of this paper is to explore how an organization can combine different types of open innovations and what are the key factors that may influence the combination of different open innovations. Design/methodology/approach The basic methodology of this paper is the longitudinal inductive analysis within the conceptual framework of the open innovation proposed by Dahlander and Gann (2010). In this case study of Xiaomi Tech Inc., the open innovation combination is investigated through examining 25 new products created between August 2010 and December 2016 in terms of four general types: acquiring, sourcing, selling and revealing open innovation. Findings In practice, the combination of different types of open innovations can be realized. A firm may combine different open innovations at three levels: a single product level, a related product cluster level and a company level. In addition, different open innovations can be combined in diverse modes. The purpose of combining different types of open innovations is to overcome the disadvantages of each type and to exploit the advantages of all different types. Many factors may affect a firm’s option of how to combine open innovations. At different development stages, a firm may make and implement corresponding strategic direction based on its innovation capacity and internal resource. For a given strategy, the firm needs to create profits and manage intellectual property in the implementation of open innovations. These factors are interacted each other, rather than isolated. Originality/value The findings of this paper are helpful for better understanding how and why an organization can combine different types of open innovations. From a managerial point of view, an organization may combine different types of open innovations to leverage advantages and avoid disadvantages of each certain type of open innovation. An appropriate combination of different open innovations can effectively improve new product development.

scholarly journals Analysis of rail yard and terminal performances

2014 ◽  
Vol 8 (2) ◽  
pp. 178-200 ◽  
Author(s):  
Marin Marinov ◽  
Leonardo Di Giovanni ◽  
Giulia Bellisai ◽  
Julian Clevermann ◽  
Anastasia Mastellou ◽  
...  
Keyword(s):  
Comparative Analysis ◽  
Critical Points ◽  
Network Performance ◽  
Logical Consequence ◽  
Time Frame ◽  
Key Factors ◽  
Railway Network ◽  
Rail Infrastructure ◽  
Different Types ◽  
Junction Points

One of the latest trends in the transport field is the increasing interest for the rejuvenation of the railway. It is considered to be a logical consequence of the gradual switch towards a more sustainable future in transports. Terminals and stations are considered to be the junction points between the various lines that constitute the railway network and can simply be described as points of arrival, departure and interchange of passengers or commodities. The most commonly used indicators that measure the level of their performance are time and cost. This study aims at exploring possible improvements that could be implemented to the infrastructure and the operation of terminals and stations in order to increase the efficiency level. Firstly, drawing upon grounded theory about rail infrastructure and terminals, a description is conducted, followed by a comparative analysis of the different types of existing terminals and stations. Secondly, the suggested improvements are presented in accordance with their time frame completion. The main contribution of this study is to illustrate the high significance of terminals, stations and yards, acknowledging them as crucial parts of the railway network, because as characterized and demonstrated in this study, their performance are key factors to the whole network performance, making the identification of their critical points and respective possible solutions, the final objective of this paper. In addition to this, emphasis is given to the need of improving and developing the existing terminal infrastructure and operations.

A New Grid Multi-Scroll Chaotic System and the Simulation Based on Labview

2012 ◽  
Vol 538-541 ◽  
pp. 2666-2669
Author(s):  
Yong Huang
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Step Function ◽  
Simulation System ◽  
Unstable System ◽  
Simulation Based ◽  
Two Parameters ◽  
The Way

In order to get the grid Multi-Scroll in the two directions, based on a simple unstable system, the way of the combination of the translational transform and step function was put forward to make the scrolls extending in the x and y directions in this paper. The quantity of scrolls can be controlled by two parameters N and M. A simulation system was designed with Labview to simulate grid Multi-Scroll chaotic system, it demonstrates the existence of grid Multi-Scroll chaotic attractor.

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