Dynamic behavior of fractional-order memristive time-delay system and image encryption application

2021 ◽  
pp. 2150271
Author(s):  
Zongli Yang ◽  
Dong Liang ◽  
Dawei Ding ◽  
Yongbing Hu
Keyword(s):  
Time Delay ◽  
Dynamic Behavior ◽  
Image Encryption ◽  
Fractional Order ◽  
Delay System ◽  
Encryption Scheme ◽  
Time Delay System ◽  
Chaotic State ◽  
Periodic State ◽  
The Stability

This paper presents dynamic behavior of a fractional-order memristive time-delay system and its application in image encryption. First, a fractional-order memristive time-delay system is proposed, and the stability and bifurcation behaviors of the system are theoretically analyzed. Some limited conditions for describing the stability interval and switching between different dynamic behaviors are derived. Second, the dynamic characteristics of the system are analyzed through the coexisting attractors, coexisting bifurcation diagrams, the Largest Lyapunov exponents (LLE), the 0-1 test. When parameters change, such as time delay and fractional order, the system transits from steady state to periodic state, single scroll chaotic state, double scroll chaotic state. Furthermore, an image encryption scheme based on the fractional-order memristive time-delay system is introduced, and some statistical features are analyzed. Finally, numerical simulations verify the validity of the theoretical analysis and safety of the image encryption scheme based on the fractional-order delayed memristive chaotic system.

A new image encryption scheme based on a simple first-order time-delay system with appropriate nonlinearity

2015 ◽  
Vol 82 (1-2) ◽  
pp. 107-117 ◽  
Author(s):  
Olfa Mannai ◽  
Rabei Bechikh ◽  
Houcemeddine Hermassi ◽  
Rhouma Rhouma ◽  
Safya Belghith
Keyword(s):  
Time Delay ◽  
Image Encryption ◽  
Delay System ◽  
Encryption Scheme ◽  
Time Delay System ◽  
First Order

On the stability bifurcation of a nonlinear time delay system

Automatica ◽  
1998 ◽  
Vol 34 (3) ◽  
pp. 375-378 ◽  
Author(s):  
Mustapha S. Fofana ◽  
David J. Lamb
Keyword(s):  
Time Delay ◽  
Delay System ◽  
Time Delay System ◽  
The Stability

Robust Fractional Order Proportional Integral Control for Large Time-Delay System

2014 ◽  
Vol 716-717 ◽  
pp. 1614-1619
Author(s):  
Rui Hao Xin ◽  
Chun Yang Wang ◽  
Xue Lian Liu ◽  
Ming Qiu Li ◽  
Duan Yuan Bai
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Delay Time ◽  
Large Time ◽  
Delay System ◽  
Order System ◽  
Time Delay System ◽  
Proportional Integral ◽  
Integral Controller ◽  
Proportional Integral Controller

In this paper, a new control method for large time delay system is proposed. Firstly, the decreasing time delay controller is used to remodel large delay time plant into small delay time plant. Then, a fractional robust proportional-integral controller (FOPI) is designed, using the phase margin and cut-off frequency at a specified point in the Bode plot of flat robust conditions, to guarantee the desired control performance and the robustness of the high order system to the gain order system. For comparison between the fractional order proportional integral controller and the traditional integer order PID (IOPID) controller, the IOPID controller is also designed following the same proposed tuning specifications. The simulation results indicates that the both designed controllers work efficiently. Furthermore, the FOPI controller makes the large time-delay system get better control effect, the system has high robustness, adaptive ability and anti-jamming ability.

scholarly journals Synchronization approach for chaotic time-varying delay system based on Wirtinger inequality

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668902
Author(s):  
Zhanshan Zhao ◽  
Meili He ◽  
Jing Zhang ◽  
Guowei Xu
Keyword(s):  
Time Delay ◽  
Stability Criterion ◽  
Delay System ◽  
Jensen Inequality ◽  
Time Delay System ◽  
Control Approach ◽  
Time Varying Delay ◽  
Wirtinger Inequality ◽  
The Stability ◽  
Varying Delay

A novel control approach based on Wirtinger inequality is designed for nonlinear chaos synchronization time delay system. In order to reduce the conservatism for the stability criterion, a Lyapunov–Krasovskii functional with triple-integral term is constructed. The improved Wirtinger inequality is used to reduce the conservative which is caused by Jensen inequality, and a stability criterion is proposed by reciprocally convex method. Furthermore, a state feedback controller is designed to synchronize the master-slave systems based on the proposed criteria through cone complementary linearization approach. Finally, a simulation for Lorenz chaos time delay system is given to prove the validity based on the proposed synchronization control approach.

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