scholarly journals Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 71
Author(s):  
Ze Wang ◽  
Guoyuan Qi
Keyword(s):  
Euler Equation ◽  
Chaotic System ◽  
Analog Circuit ◽  
Dynamical Behavior ◽  
Conservative System ◽  
Trial And Error ◽  
Modeling And Analysis ◽  
System A ◽  
Extensive Variable ◽  
Definition Of

In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed four-dimensional (4D) Euler equation. The generalized Hamiltonian energy function has been given, and it is composed of conservative and non-conservative parts of the Hamiltonian. The Hamiltonian of the Euler equation remains constant, while the three-terminal memristor’s Hamiltonian is mutative, causing non-conservation in energy. Through proof, only centers or saddles equilibria exist, which meets the definition of the conservative system. A non-Hamiltonian conservative chaotic system is proposed. The Hamiltonian of the conservative part determines whether the system can produce chaos or not. The non-conservative part affects the dynamic of the system based on the conservative part. The chaotic and quasiperiodic orbits are generated when the system has different Hamiltonian levels. Lyapunov exponent (LE), Poincaré map, bifurcation and Hamiltonian diagrams are used to analyze the dynamical behavior of the non-Hamiltonian conservative chaotic system. The frequency and initial values of the system have an extensive variable range. Through the mechanism adjustment, instead of trial-and-error, the maximum LE of the system can even reach an incredible value of 963. An analog circuit is implemented to verify the existence of the non-Hamiltonian conservative chaotic system, which overcomes the challenge that a little bias will lead to the disappearance of conservative chaos.

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.

scholarly journals Zur exakten Behandlung von kollektiven Rotationen Teil A: Theorie / On the Exact Treatment of Collective Rotations Part A: Theory

1973 ◽  
Vol 28 (2) ◽  
pp. 206-215
Author(s):  
Hanns Ruder
Keyword(s):  
Coordinate System ◽  
Perturbation Expansion ◽  
Rotational Energy ◽  
The Body ◽  
System A ◽  
N Body Problem ◽  
Definition Of ◽  
Fixed System ◽  
Body Fixed Coordinate System ◽  
Groundstate Energy

Basic in the treatment of collective rotations is the definition of a body-fixed coordinate system. A kinematical method is derived to obtain the Hamiltonian of a n-body problem for a given definition of the body-fixed system. From this exact Hamiltonian, a consequent perturbation expansion in terms of the total angular momentum leads to two exact expressions: one for the collective rotational energy which has to be added to the groundstate energy in this order of perturbation and a second one for the effective inertia tensor in the groundstate. The discussion of these results leads to two criteria how to define the best body-fixed coordinate system, namely a differential equation and a variational principle. The equivalence of both is shown.

XV.—The Placoderm Fish Rhachiosteus pterygiatus Gross and its Relationships

1966 ◽  
Vol 66 (15) ◽  
pp. 377-392 ◽  
Author(s):  
Roger S. Miles
Keyword(s):  
Sensory System ◽  
System A ◽  
The Family ◽  
Definition Of

SynopsisThe holotype and only known specimen of Rhachiosteus pterygiatus Gross is partially redescribed and new restorations are given. Attention is drawn to important points in its osteology and the possible development of a cutaneous sensory system. A definition of the family Rhachiosteidsæ Stensiö is given. This family differs from all other described groups of euarthrodires in the lack of posterior lateral and posterior dorsolateral flank plates. Rhachiosteus is a pachyosteomorph brachythoracid, as defined in the text, and may be fairly closely related in some way to the (coccosteomorph) family Coccosteidsæ. There is no indication that it is closely related to any other known pachyosteomorph, or to other groups of arthrodires, such as the Rhenanida and Ptyctodontida, in which there are no posterior flank plates.

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.

Optimal Synchronization of a Memristive Chaotic Circuit

2016 ◽  
Vol 26 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Michaux Kountchou ◽  
Patrick Louodop ◽  
Samuel Bowong ◽  
Hilaire Fotsin ◽  
Jurgen Kurths
Keyword(s):  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Dynamical Properties ◽  
Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

scholarly journals CONSTRUCTION OF MINIMAX CONTROL FOR ALMOST CONSERVATIVE CONTROLLED DYNAMIC SYSTEMS WITH THE LIMITED PERTURBATIONS

2017 ◽  
Vol 2 ◽  
pp. 9-15
Author(s):  
Iryna Svyatovets
Keyword(s):  
Riccati Equation ◽  
Infinite System ◽  
Conservative System ◽  
Coefficient Matrix ◽  
Necessary Condition ◽  
Existence Of A Solution ◽  
Minimax Control ◽  
System Of Matrix Equations ◽  
System A ◽  
The Matrix

The problem is considered for constructing a minimax control for a linear stationary controlled dynamical almost conservative system (a conservative system with a weakly perturbed coefficient matrix) on which an unknown perturbation with bounded energy acts. To find the solution of the Riccati equation, an approach is proposed according to which the matrix-solution is represented as a series expansion in a small parameter and the unknown components of this matrix are determined from an infinite system of matrix equations. A necessary condition for the existence of a solution of the Riccati equation is formulated, as well as theorems on additive operations on definite parametric matrices. A condition is derived for estimating the parameter appearing in the Riccati equation. An example of a solution of the minimax control problem for a gyroscopic system is given. The system of differential equations, which describes the motion of a rotor rotating at a constant angular velocity, is chosen as the basis.

scholarly journals Modeling and analysis of mission thread of weapon system of systems based on O-PPN

2021 ◽  
Vol 39 (1) ◽  
pp. 197-207
Author(s):  
Yuqi Chen ◽  
Tingxue Xu ◽  
Xiaotong Zhao ◽  
Cheng Lu
Keyword(s):  
Petri Net ◽  
Success Probability ◽  
Failure Criteria ◽  
Performance Degradation ◽  
Operation Performance ◽  
Modeling And Analysis ◽  
Reliability Parameters ◽  
Mission Success ◽  
Definition Of ◽  
Equipment System

Aiming at the problem that the current WSoS mission modeling and analysis methods are difficult to describe the property of multi-state of each equipment system, combining with Petri net and Markov process, an O-PPN based mission thread modeling and analysis method is proposed in this paper. Based on the definition of WSoS, the mission of WSoS is formally described. To improve the traditional Petri net, an operation performance Petri net (O-PPN) is constructed, in order to meet the modeling needs of the general mission thread of the WSoS; and aiming at the problems of the performance degradation of the equipment system and the possible "ahead of time" state, the performance degradation model of the equipment system based on Markov is constructed. The corresponding state probability set is obtained by inputting the reliability parameters of each equipment system. And according to the requirements of each operation in the mission thread for the performance level of each equipment system and combined with the mission success and failure criteria of the combat task and operation, the mission success probability of the whole WSoS is calculated. Finally, the feasibility of the proposed method is verified by the simulation of the case.

scholarly journals SOCIO-GEOGRAPHICAL ESSENCE OF THE MILITARY SPHERE OF UKRAINE

2020 ◽  
pp. 50-57
Author(s):  
Taras Kravets
Keyword(s):  
Armed Forces ◽  
Industrial Complex ◽  
Modeling And Analysis ◽  
Military Industrial Complex ◽  
Military Geography ◽  
Literary Sources ◽  
Methodological Problems ◽  
Definition Of ◽  
The Military ◽  
General Method

The purpose of the article is to analyze the existing approaches to understanding the terms military sphere, military-industrial complex, defense-industrial complex, security and defense sector, military sector, determining the positioning of the military sphere and its position relative to other natural-geographical areas, joints and overlaps, identification of its functions and problems that interfere with proper functioning. Development of directions and prospects for the development of the military sphere and the Armed Forces of Ukraine in general. Method. The research was conducted on the basis of the analysis of available literature sources on this topic and the application of a spherical approach to the analysis of the positioning of the military sphere and the definition of its components. The available domestic and foreign literary sources and the ratio of these concepts within this literature are studied. Results. Theoretical and methodological problems of comparing concepts related to the military sphere and their interchangeability and interconnectedness are studied. The scheme of correlation of concepts of military sphere, defense-industrial complex and military-industrial complex is offered. Based on the spherical approach, we propose a scheme of the military sphere, which we consider as a sphere formed within the geosphere at the junction of social and natural spheres, at the intersection of demographic, informational, spiritual, environmental, technical, economic, political and social spheres. Within each oblast forming the sphere, three main sectors with the greatest influence on the military sphere are singled out. Six main functions of the sphere are singled out and arranged in order of importance on the basis of the proposed scheme. Scientific novelty. The need for this study is due to the fact that despite the fact that since 2014 and to date, fighting has been going on in the east of our country, in many universities the discipline of military geography and related disciplines is being stolen, the term military sphere has not been proposed. clear positioning of the military sphere among other social spheres. To date, the functions performed by the military sphere and the factors contributing to the improvement and development of this sphere have not been determined, which is what led to the implementation of this study. Practical meaning. Based on modeling and analysis, the main areas that affect the military sphere as such and to what extent are identified, the areas of greatest influence and sectors of influence within the regions are identified. The functions of the military sphere and the main factors influencing its development and transformation are highlighted, as well as what measures need to be implemented to improve the situation. The results of the research are developed for planning by the state structures of the program of development of the military sphere and for teaching the discipline "Military Geography". The geographical features of the military sphere are singled out, to which the greatest attention should be paid when analyzing the transformation of the military sphere.

scholarly journals Bank Stability Measures in Dual Banking System: A Critical Review

2019 ◽  
Vol 5 (2) ◽  
pp. 59
Author(s):  
Norzitah Abdul Karim ◽  
Amirul Afiff Muhamat ◽  
Azreen Roslan ◽  
Sharifah Faigah Syed Alwi ◽  
Mohamad Nizam Jaafar
Keyword(s):  
Global Financial Crisis ◽  
Financial Institution ◽  
Banking System ◽  
Banking Supervision ◽  
Basel Committee ◽  
System A ◽  
Overall Stability ◽  
Regulatory Bodies ◽  
Banking Stability ◽  
Definition Of

The 2007-2009 Global Financial Crisis showed that despite reported as ‘healthy’ financial institution prior to crisis had indeed suffered many problems including liquidity during the crisis. Thus, there is confusion on the healthy financial institutions, leading to loss of confidence on the overall stability of the banking system. Thus, there is an urgent need to review the current measures of financial as well as banking stability. This paper aims to look at the definition of ‘stability’ used in the academic researches and by different regulatory bodies, like International Monetary Fund, Basel Committee for Banking Supervision (BCBS) and central banks in selected countries with dual banking systems. It is then, critically review indicators used as measures of financial as well as banking stability. This review is hope to identify areas of strengths as well as weaknesses of the current measures of stability and serves as foundation for further research in future.

scholarly journals Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

2021 ◽  
Author(s):  
Hegui Zhu ◽  
Jiangxia Ge ◽  
Wentao Qi ◽  
Xiangde Zhang ◽  
Xiaoxiong Lu
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Encryption Algorithm ◽  
Topological Transitivity ◽  
Detailed Simulation ◽  
Definition Of ◽  
Image Encryption Algorithm ◽  
Sensitivity To Initial Conditions

Abstract Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

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