scholarly journals A Novel Megastable Hamiltonian System with Infinite Hyperbolic and Nonhyperbolic Equilibria

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Gervais Dolvis Leutcho ◽  
Theophile Fonzin Fozin ◽  
Alexis Nguomkam Negou ◽  
Zeric Tabekoueng Njitacke ◽  
Viet-Thanh Pham ◽  
...  
Keyword(s):  
Hamiltonian System ◽  
Nonlinear Analysis ◽  
Chaotic Systems ◽  
Engineering Application ◽  
Ergodic Property ◽  
Dissipative Systems ◽  
Conservative Oscillator ◽  
Analysis Tools ◽  
The Stability ◽  
New System

The dimension of the conservative chaotic systems is an integer and equals the system dimension, which brings about a better ergodic property and thus have potentials in engineering application than the dissipative systems. This paper investigates the phenomenon of megastability in a unique and simple conservative oscillator with infinite of hyperbolic and nonhyperbolic equilibria. Using traditional nonlinear analysis tools, we found that the introduced oscillator possesses an invariable energy and displays either self-excited or hidden dynamics depending on the stability of its equilibria. Besides, the conservative nature of the new system is validated using theoretical measurement. Furthermore, an analog simulator of the oscillator is built and simulated in the PSpice environment to confirm that the previous results were not artifacts.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

2006 ◽  
Vol 17 (01) ◽  
pp. 65-73 ◽  
Author(s):  
SHIRO SAWADA
Keyword(s):  
Nonlinear Analysis ◽  
Relative Velocity ◽  
Velocity Model ◽  
Fundamental Diagram ◽  
Optimal Velocity ◽  
Traffic Jam ◽  
Optimal Velocity Model ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Good Agreement

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

scholarly journals Active Sliding Mode for Synchronization of a Wide Class of Four-Dimensional Fractional-Order Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Wang ◽  
Yuangui Zhou ◽  
Jianyi Xue ◽  
Delan Zhu
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Wide Class ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Order System ◽  
Fractional Order Calculus ◽  
Simulation Results ◽  
The Stability

We focus on the synchronization of a wide class of four-dimensional (4-D) chaotic systems. Firstly, based on the stability theory in fractional-order calculus and sliding mode control, a new method is derived to make the synchronization of a wide class of fractional-order chaotic systems. Furthermore, the method guarantees the synchronization between an integer-order system and a fraction-order system and the synchronization between two fractional-order chaotic systems with different orders. Finally, three examples are presented to illustrate the effectiveness of the proposed scheme and simulation results are given to demonstrate the effectiveness of the proposed method.

The effects of drivers’ aggressive characteristics on traffic stability from a new car-following model

2016 ◽  
Vol 30 (18) ◽  
pp. 1650243 ◽  
Author(s):  
Guanghan Peng ◽  
Li Qing
Keyword(s):  
Stability Analysis ◽  
Nonlinear Analysis ◽  
Traffic Flow ◽  
Linear Stability Analysis ◽  
Stable Condition ◽  
Mkdv Equation ◽  
Stable Region ◽  
Car Following ◽  
Car Following Model ◽  
The Stability

In this paper, a new car-following model is proposed by considering the drivers’ aggressive characteristics. The stable condition and the modified Korteweg-de Vries (mKdV) equation are obtained by the linear stability analysis and nonlinear analysis, which show that the drivers’ aggressive characteristics can improve the stability of traffic flow. Furthermore, the numerical results show that the drivers’ aggressive characteristics increase the stable region of traffic flow and can reproduce the evolution and propagation of small perturbation.

scholarly journals Study of the Stability Control of the Rock Surrounding Double-Key Strata Recovery Roadways in Shallow Seams

2019 ◽  
Vol 2019 ◽  
pp. 1-21 ◽  
Author(s):  
Cheng Zhu ◽  
Yong Yuan ◽  
Zhongshun Chen ◽  
Zhiheng Liu ◽  
Chaofeng Yuan
Keyword(s):  
Engineering Application ◽  
Stability Control ◽  
Surrounding Rock ◽  
Control Effect ◽  
Pressure Relief ◽  
Support Design ◽  
Key Strata ◽  
Fracture Development ◽  
Surrounding Rock Control ◽  
The Stability

The stability control of the rock surrounding recovery roadways guarantees the safety of the extraction of equipment. Roof falling and support crushing are prone to occur in double-key strata (DKS) faces in shallow seams during the extraction of equipment. Therefore, this paper focuses on the stability control of the rock surrounding DKS recovery roadways by combining field observations, theoretical analysis, and numerical simulations. First, pressure relief technology, which can effectively release the accumulated rock pressure in the roof, is introduced according to the periodic weighting characteristics of DKS roofs. A reasonable application scope and the applicable conditions for pressure relief technology are given. Considering the influence of the eroded area on the roof structure, two roof mechanics models of DKS are established. The calculation results show that the yield load of the support in the eroded area is low. A scheme for strengthening the support with individual hydraulic props is proposed, and then, the support design of the recovery roadway is improved based on the time effects of fracture development. The width of the recovery roadway and supporting parameters is redesigned according to engineering experience. Finally, constitutive models of the support and compacted rock mass in the gob are developed with FLAC3D software to simulate the failure characteristics of the surrounding rock during pressure relief and equipment extraction. The surrounding rock control effects of two support designs and three extraction schemes are comprehensively evaluated. The results show that the surrounding rock control effect of Scheme 1, which combines improved support design and the bidirectional extraction of equipment, is the best. Engineering application results show that Scheme 1 realizes the safe extraction of equipment. The research results can provide a reference and experience for use in the stability control of rock surrounding recovery roadways in shallow seams.

Calculation of Static Safety Coefficient about Loess Cave

2011 ◽  
Vol 189-193 ◽  
pp. 2366-2370
Author(s):  
Jun Hong Li
Keyword(s):  
Finite Element ◽  
Yield Criterion ◽  
Soil Layer ◽  
Engineering Application ◽  
Static Stability ◽  
Strength Reduction ◽  
Engineering Practice ◽  
Stability Calculation ◽  
Safety Coefficient ◽  
The Stability

For the loess cave characteristics, such as the thin coverage soil layer at the hole top, the poor self-stabilizing capacity, the large disturbance deformation after excavation and the easy collapse, thus in this paper, the loess cave safety factor is obtained by the method of strength reduction. And the stability calculation analysis is much more perfect. The Northwest Area Lishi loess cave is used in this paper, and the idea of strength reduction finite element method is applied, based on the Drucker-Prager yield criterion, the loess cave static stability analysis is made by the software of ANSYS.The results show that the actual situation can be reflected by the method of finite element strength subtraction. And the obtained loess cave stability coefficient is much closer to the actual steady state, thus showing the certain advantages of stability analysis.The method is also adopted in this paper. And its feasibility can be applied to the engineering practice, also a theoretical basis of reference is provided for engineering application.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals Hybrid Passivity Based and Fuzzy Type-2 Controller for Chaotic and Hyper-Chaotic Systems

2017 ◽  
Vol 11 (2) ◽  
pp. 96-103 ◽  
Author(s):  
Fernando Serrano ◽  
Josep M. Rossell
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Control Strategy ◽  
Chaotic Systems ◽  
Control Law ◽  
Four Dimensions ◽  
Design Requirements ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper a hybrid passivity based and fuzzy type-2 controller for chaotic and hyper-chaotic systems is presented. The proposed control strategy is an appropriate choice to be implemented for the stabilization of chaotic and hyper-chaotic systems due to the energy considerations of the passivity based controller and the flexibility and capability of the fuzzy type-2 controller to deal with uncertainties. As it is known, chaotic systems are those kinds of systems in which one of their Lyapunov exponents is real positive, and hyper-chaotic systems are those kinds of systems in which more than one Lyapunov exponents are real positive. In this article one chaotic Lorentz attractor and one four dimensions hyper-chaotic system are considered to be stabilized with the proposed control strategy. It is proved that both systems are stabilized by the passivity based and fuzzy type-2 controller, in which a control law is designed according to the energy considerations selecting an appropriate storage function to meet the passivity conditions. The fuzzy type-2 controller part is designed in order to behave as a state feedback controller, exploiting the flexibility and the capability to deal with uncertainties. This work begins with the stability analysis of the chaotic Lorentz attractor and a four dimensions hyper-chaotic system. The rest of the paper deals with the design of the proposed control strategy for both systems in order to design an appropriate controller that meets the design requirements. Finally, numerical simulations are done to corroborate the obtained theoretical results.

Robust Synchronization of Fractional-Order Arneodo Chaotic Systems Using a Fractional Sliding Mode Control Strategy

2018 ◽  
pp. 1-22
Author(s):  
Samir Ladaci ◽  
Karima Rabah ◽  
Mohamed Lashab
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Mode Control ◽  
Control Configuration ◽  
The Stability

This chapter investigates a new control design methodology for the synchronization of fractional-order Arneodo chaotic systems using a fractional-order sliding mode control configuration. This class of nonlinear fractional-order systems shows a chaotic behavior for a set of model parameters. The stability analysis of the proposed fractional-order sliding mode control law is performed by means of the Lyapunov stability theory. Simulation examples on fractional-order Arneodo chaotic systems synchronization are provided in presence of disturbances and noises. These results illustrate the effectiveness and robustness of this control design approach.

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