scholarly journals Dynamic Analysis and Robust Control of a Chaotic System with Hidden Attractor

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Huaigu Tian ◽  
Zhen Wang ◽  
Peijun Zhang ◽  
Mingshu Chen ◽  
Yang Wang
Keyword(s):  
Numerical Simulation ◽  
Robust Control ◽  
Theoretical Analysis ◽  
Chaotic System ◽  
Finite Time ◽  
Original System ◽  
Slave System ◽  
Hidden Attractor ◽  
Time Stability ◽  
Finite Time Stability

In this paper, a 3D jerk chaotic system with hidden attractor was explored, and the dissipativity, equilibrium, and stability of this system were investigated. The attractor types, Lyapunov exponents, and Poincare section of the system under different parameters were analyzed. Additionally, a circuit was carried out, and a good similarity between the circuit experimental results and the theoretical analysis testifies the feasibility and practicality of the original system. Furthermore, a robust feedback controller was designed based on the finite-time stability theory, which guarantees the synchronization of 3D jerk master-slave system in finite time and asymptotically converges to the origin. Finally, we also give verification for the discussion in this paper by numerical simulation.

Adaptive Projective Synchronization of the New Three-Dimensional Chaotic System

2013 ◽  
Vol 321-324 ◽  
pp. 921-924 ◽  
Author(s):  
Su Hai Huang
Keyword(s):  
Chaotic System ◽  
Finite Time ◽  
Chaos Synchronization ◽  
Three Dimensional ◽  
Projective Synchronization ◽  
Time Stability ◽  
Finite Time Stability ◽  
Adaptive Technique ◽  
New Chaotic System ◽  
Synchronization Scheme

This paper deals with the finite-time chaos synchronization of the new chaotic system [with uncertain parameters. Based on the finite-time stability theory and adaptive technique, a controller has been designed to realize finite-time chaos projective synchronization and parameter identification. Moreover, numerical simulation result is included to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

scholarly journals Finite-time stability of discrete-time systems with time-varying delay

2012 ◽  
Vol 18 (4-1) ◽  
pp. 525-533 ◽  
Author(s):  
Sreten Stojanovic ◽  
Dragutin Debeljkovic ◽  
Nebojsa Dimitrijevic
Keyword(s):  
Finite Time ◽  
Linear Time ◽  
Original System ◽  
Delay Systems ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Maximum Delay ◽  
Varying Delay

Finite-time stability can be used in all applications where large values of the state are not acceptable. In this paper, finite-time stability problem for a class of linear time-varying delay systems is studied. Based on Lyapunov-like functions method and using an appropriate model transformation of the original system, the sufficient delay-dependent finite-time stability conditions are derived. The criteria are presented in the form of LMIs, which are dependent on the minimum and maximum delay bounds. The numerical examples are presented to illustrate the applicability of the developed results.

scholarly journals Finite-Time Stability Criteria for a Class of High-Order Fractional Cohen–Grossberg Neural Networks with Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhanying Yang ◽  
Jie Zhang ◽  
Junhao Hu ◽  
Jun Mei
Keyword(s):  
Neural Networks ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Finite Time ◽  
Analytical Techniques ◽  
Stability Criteria ◽  
Time Stability ◽  
Practical Applications ◽  
Finite Time Stability

This paper focuses on a class of delayed fractional Cohen–Grossberg neural networks with the fractional order between 1 and 2. Two kinds of criteria are developed to guarantee the finite-time stability of networks based on some analytical techniques. This method is different from those in some earlier works. Moreover, the obtained criteria are expressed as some algebraic inequalities independent of the Mittag–Leffler functions, and thus, the calculation is relatively simple in both theoretical analysis and practical applications. Finally, the feasibility and validity of obtained results are supported by the analysis of numerical simulations.

FINITE-TIME CHAOS SYNCHRONIZATION OF A NEW HYPERCHAOTIC LORENZ SYSTEM

2013 ◽  
Vol 27 (09) ◽  
pp. 1350033 ◽  
Author(s):  
XINGYUAN WANG ◽  
XULONG GAO ◽  
LULU WANG
Keyword(s):  
Theoretical Analysis ◽  
Finite Time ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Lorenz System ◽  
Time Stability ◽  
Robust Controller ◽  
Finite Time Stability ◽  
Error System ◽  
Hyperchaotic Lorenz System

This paper deals with the finite-time chaos synchronization of a new hyperchaotic Lorenz system. Based on the finite-time stability theory, a simple and robust controller is proposed to realize finite-time chaos synchronization for the hyperchaotic Lorenz system. Theoretical analysis proved that the scheme can ensure the error system globally finite-time stable. Numerical simulations are provided to show the effectiveness of the proposed schemes.

Finite-Time Chaos Control of Lorenz Chaotic System Based on the Passive Control Teachnique

2013 ◽  
Vol 397-400 ◽  
pp. 1345-1350
Author(s):  
Feng Liu
Keyword(s):  
Chaotic System ◽  
Finite Time ◽  
Chaos Control ◽  
Passive Control ◽  
Control Method ◽  
Control Technique ◽  
Time Stability ◽  
Finite Time Stability ◽  
Lorenz Chaotic System ◽  
Robust To Noise

Finite-time chaos control of Lorenz chaotic system applying the passive control method is investigated in this paper. Based on the finite-time stability theory and the passive control technique, the passive controller are proposed to realize finite-time chaos control of Lorenz chaotic system. The controller is robust to noise. Both theoretical and numerical simulations show the effectiveness of the proposed method.

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