Dynamical behavior and reduced-order combination synchronization of a novel chaotic system

2017 ◽  
Vol 6 (3) ◽  
pp. 1160-1174 ◽  
Author(s):  
Khan Ayub ◽  
Shikha
Keyword(s):  
Chaotic System ◽  
Dynamical Behavior ◽  
Reduced Order ◽  
Combination Synchronization

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.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

Jacobi analysis for an unusual 3D autonomous system

2020 ◽  
Vol 17 (04) ◽  
pp. 2050062 ◽  
Author(s):  
Chunsheng Feng ◽  
Qiujian Huang ◽  
Yongjian Liu
Keyword(s):  
Chaotic System ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Chen System ◽  
Parameter Region ◽  
Stable Equilibria ◽  
The Lorenz System ◽  
Deviation Vector

Little seems to be known about the study of the chaotic system with only Lyapunov stable equilibria from the perspective of differential geometry. Therefore, this paper presents Jacobi analysis of an unusual three-dimensional (3D) autonomous chaotic system. Under certain parameter conditions, this system has positive Lyapunov exponents and only two linear stable equilibrium points, which means that chaotic attractor and Lyapunov stable equilibria coexist. The dynamical behavior of the deviation vector near the whole trajectories (including all equilibrium points) is analyzed in detail. The results show that the value of the deviation curvature tensor at equilibrium points is only related to parameters; the two equilibrium points of the system are Jacobi stable if the parameters satisfy certain conditions. Particularly, for a specific set of parameters, the linear stable equilibrium points of the system are always Jacobi unstable. A periodic orbit that is Lyapunov stable is also proven to be always Jacobi unstable. Next, Jacobi-stable regions of the Lorenz system, the Chen system and the system under study are compared for specific parameters. It can be found that although these three chaotic systems are very similar, their regions of Jacobi stable parameters are much different. Finally, by comparing Jacobi stability with Lyapunov stability, the obtained results demonstrate that the Jacobi stable parameter region is basically symmetric with the Lyapunov stable parameter region.

scholarly journals Reduced-Order Antisynchronization of Chaotic Systems via Adaptive Sliding Mode Control

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Wafaa Jawaada ◽  
M. S. M. Noorani ◽  
M. Mossa Al-Sawalha ◽  
M. Abdul Majid
Keyword(s):  
Sliding Mode Control ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Dynamical Evolution ◽  
Adaptive Sliding Mode Control ◽  
Reduced Order ◽  
Adaptive Sliding Mode ◽  
Mode Control ◽  
Adaptive Sliding Mode Controller

A novel reduced-order adaptive sliding mode controller is developed and experimented in this paper to antisynchronize two different chaotic systems with different order. Based upon the parameters modulation and the adaptive sliding mode control techniques, we show that dynamical evolution of third-order chaotic system can be antisynchronized with the projection of a fourth-order chaotic system even though their parameters are unknown. The techniques are successfully applied to two examples: firstly Lorenz (4th-order) and Lorenz (3rd-order) and secondly the hyperchaotic Lü (4th-order) and Chen (3rd-order). Theoretical analysis and numerical simulations are shown to verify the results.

Seismic Response Analysis on a Chaotic System

2013 ◽  
Vol 639-640 ◽  
pp. 911-916
Author(s):  
Cui Xiang Liang
Keyword(s):  
Seismic Response ◽  
Chaotic System ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Response Analysis ◽  
Bifurcation Diagrams ◽  
Seismic Response Analysis ◽  
Nonlinear Seismic Response ◽  
Hyperbolic Equilibrium ◽  
Hyperbolic Equilibrium Point

This paper is concerned with the dynamical behavior of a chaotic system which is a model for seismic response of structures. The local bifurcation of the non-hyperbolic equilibrium point of the chaotic system is investigated by using center manifold method. The transcritical bifurcation is analyzed in detail. Based on numerical simulations, spectrums of maximal Lyapunov exponent and the bifurcation diagrams are presented for the dynamic analysis. The method proposed can be used as a reference of nonlinear seismic response analysis.

scholarly journals A Novel Memductor-Based Chaotic System and Its Applications in Circuit Design and Experimental Validation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Li Xiong ◽  
Yanjun Lu ◽  
Yongfang Zhang ◽  
Xinguo Zhang
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Experimental Validation ◽  
Control Method ◽  
Dynamical Behavior ◽  
Chaotic Circuit ◽  
Initial State ◽  
Error System ◽  
The Stability ◽  
The Mathematical Model

This paper is expected to introduce a novel memductor-based chaotic system. The local dynamical entities, such as the basic dynamical behavior, the divergence, the stability of equilibrium set, and the Lyapunov exponent, are all investigated analytically and numerically to reveal the dynamic characteristics of the new memductor-based chaotic system as the system parameters and the initial state of memristor change. Subsequently, an active control method is derived to study the synchronous stability of the novel memductor-based chaotic system through making the synchronization error system asymptotically stable at the origin. Further to these, a memductor-based chaotic circuit is designed, realized, and applied to construct a new memductor-based secure communication circuit by employing the basic electronic components and memristor. Furthermore, the design principle of the memductor-based chaotic circuit is thoroughly analyzed and the concept of “the memductor-based chaotic circuit defect quantification index” is proposed for the first time to verify whether the chaotic output is consistent with the mathematical model. A good qualitative agreement is shown between the simulations and the experimental validation results.

scholarly journals Reduced order hybrid function projective combination synchronization of three Josephson junctions

2014 ◽  
Vol 24 (1) ◽  
pp. 99-113 ◽  
Author(s):  
Kayode. S. Ojo ◽  
Abdulahi N. Njah ◽  
Samuel T. Ogunjo ◽  
Olasunkanmi I. Olusola
Keyword(s):  
Josephson Junction ◽  
Josephson Junctions ◽  
Chaotic Systems ◽  
Second Order ◽  
Backstepping Technique ◽  
Third Order ◽  
Reduced Order ◽  
Combination Synchronization ◽  
Response System ◽  
Hybrid Function

Abstract In this paper, we examine reduced order hybrid function projective combination synchronization of three chaotic systems consisting of: (i) two third chaotic Josephson junctions as drives and one second order chaotic Josephson junction as response system; (ii) one third order chaotic Josephson junction as the drive and two second order chaotic Josephson junctions as the slaves using active backstepping technique. The analytic results confirm the realization of reduced order hybrid function projective combination synchronization using active backstepping technique. Numerical simulations are performed to validate the analytical results.

Advanced Natural Circulation Reduced Order Model With Inclined Channel for Low Pressure Conditions

2018 ◽  
Author(s):  
René Manthey ◽  
Alexander Knospe ◽  
Carsten Lange ◽  
Christoph Schuster ◽  
Antonio Hurtado
Keyword(s):  
Reference Model ◽  
Nonlinear Dynamical Systems ◽  
Natural Circulation ◽  
Dynamical Behavior ◽  
Low Pressure ◽  
Reduced Order Model ◽  
Circulation System ◽  
Order Model ◽  
Two Phase ◽  
Reduced Order

Natural circulation with two-phase flow is a nonlinear dynamical systems, which can show a very complex and strange behavior under specific conditions. The application of stability analysis requires a large computational effort and is cumbersome in case of prediction the dynamical behavior by system codes alone. Therefore, model order reduction techniques are used to compensate this disadvantage by coupling with a bifurcation code such as MatCont. A reduced order model is derived by employing the POD-method to analyze the stability landscape of a low pressure natural circulation system representing passive safety systems such as the containment cooling condenser. The required full order model contains a classical natural circulation loop with a heated section and a riser. The two-phase region is modeled by a drift-flux mixture model. The reliability of the FOM is investigated by comparison with a reference model by the validated system code ATHLET.

ASYMPTOTIC ANALYSIS OF A NEW PIECEWISE-LINEAR CHAOTIC SYSTEM

2002 ◽  
Vol 12 (01) ◽  
pp. 147-157 ◽  
Author(s):  
M. A. AZIZ-ALAOUI ◽  
GUANRONG CHEN
Keyword(s):  
Power Spectrum ◽  
Asymptotic Analysis ◽  
Lyapunov Exponents ◽  
Chaotic System ◽  
Continuous Time ◽  
Piecewise Linear ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Numerical Examples

Dynamical behavior of a new piecewise-linear continuous-time three-dimensional autonomous chaotic system is studied. System equilibria and their stabilities are discussed. Routes to chaos and bifurcations of the system are demonstrated with various numerical examples, where the chaotic features are justified numerically via computing the system fractal dimensions, Lyapunov exponents and power spectrum.

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