American Institute of Mathematical Sciences

November  2019, 2(4): 333-346. doi: 10.3934/mfc.2019021

A single finite-time synchronization scheme of time-delay chaotic system with external periodic disturbance

 1 Springfield, MO 65801-2604, USA 2 Springfield, MO 65810, USA

* Corresponding author: sxryctc@163.com

Published  December 2019

Fund Project: The first author is supported by NSF grant 11872327 and 51777180

In this paper, dynamical behaviors of three-dimensional chaotic system with time-delay and external periodic disturbance are investigated. When the periodic perturbation term and time-delay are added, the system presents more abundant dynamic behaviors, which can be switched between periodic state and chaotic state. Based on Lyapunov stability theory, a sufficient condition for finite-time synchronization is given. A single controller is proposed to realize finite-time synchronization of time-delay chaotic system with external periodic disturbance. The addressed scheme is provided in the form of linear inequality which is simple and easy to be realized. At the same time, it also displays that when delay term $\tau$ takes different values, the time of synchronization shows certain difference. The feasibility and effectiveness of the finite-time synchronization method is verified by theoretical analysis and numerical simulation.

Citation: Juanjuan Huang, Yan Zhou, Xuerong Shi, Zuolei Wang. A single finite-time synchronization scheme of time-delay chaotic system with external periodic disturbance. Mathematical Foundations of Computing, 2019, 2 (4) : 333-346. doi: 10.3934/mfc.2019021
References:

show all references

References:
Phase trajectory and the time series of Eq.(9) with $a = 15,b = 3,c = 7$ (a) ($x_1,x_2$) (b) ($t ,x_1$)
Phase trajectory and the time series of Eq.(9) with $a = 15,b = 0.91,c = 7$ (a) ($x_1,x_2$) (b) ($t ,x_1$)
Phase trajectory and the time series of Eq.(9) with $a = 15,b = 0.5,c = 7$ (a) ($x_1,x_2$) (b) ($t ,x_1$)
Phase trajectory and the time series of Eq.(9) with $a = 15,b = 3,c = 2$ (a) ($x_1,x_2$) (b) ($t ,x_1$)
Phase trajectory and the time series of Eq.(10) with $a = 15,b = 0.91,c = 7,A = 10,\omega = 0.001$ (a) ($x_1,x_2$) (b) ($t ,x_1$)
Phase trajectory and the time series of Eq.(10) with $a = 15,b = 3,c = 7,A = 100,\omega = 0.001$ (a) ($x_1,x_2$) (b) ($t ,x_1$)
Phase trajectory and the time series of Eq.(11) with $a = 15,b = 0.91,c = 7,A = 10,\omega = 0.001,\tau = 0.3$

(a) ($x_1,x_2$) (b) ($t ,x_1$)

Phase trajectory and the time series of Eq.(11) with $a = 15,b = 3,c = 7,A = 0.1,\omega = 0.001,\tau = 0.2$

(a) ($x_1,x_2$) (b) ($t ,x_1$)

Phase trajectory and the time series of Eq.(11) with $a = 15,b = 3,c = 7,A = 0.1,\omega = 0.001,\tau = 0.3$

(a) ($x_1,x_2$) (b) ($t ,x_1$)

2D overview chaotic attractor and the chaotic time series of Eq.(11) with $\tau = 0.005$ (a) ($x_1,x_2$) (b) ($t ,x_1$)
2D overview chaotic attractor and the chaotic time series of Eq.(11) with $\tau = 0.3$ (a) ($x_1,x_2$) (b) ($t ,x_1$)
The error dynamics between systems (11) and (12) with $\tau = 0.3$ (a) $e_1$ (b) $e_2$ (b) $e_3$
The error states $e_1$ between systems (11) and (12) with $\tau = 0.005,\quad\tau = 0.05\quad and \quad \tau = 0.3$
The error states $e_2$ between systems (11) and (12) with $\tau = 0.005,\quad\tau = 0.05\quad and \quad \tau = 0.3$
The error states $e_3$ between systems (11) and (12) with $\tau = 0.005,\quad \tau = 0.05\quad and \quad \tau = 0.3$
 [1] Tingting Su, Xinsong Yang. Finite-time synchronization of competitive neural networks with mixed delays. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3655-3667. doi: 10.3934/dcdsb.2016115 [2] Zhong-Jie Han, Gen-Qi Xu. Dynamical behavior of networks of non-uniform Timoshenko beams system with boundary time-delay inputs. Networks & Heterogeneous Media, 2011, 6 (2) : 297-327. doi: 10.3934/nhm.2011.6.297 [3] Arno Berger. On finite-time hyperbolicity. Communications on Pure & Applied Analysis, 2011, 10 (3) : 963-981. doi: 10.3934/cpaa.2011.10.963 [4] Jianjun Paul Tian. Finite-time perturbations of dynamical systems and applications to tumor therapy. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 469-479. doi: 10.3934/dcdsb.2009.12.469 [5] Arno Berger, Doan Thai Son, Stefan Siegmund. Nonautonomous finite-time dynamics. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 463-492. doi: 10.3934/dcdsb.2008.9.463 [6] J. C. Robinson. A topological time-delay embedding theorem for infinite-dimensional cocycle dynamical systems. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 731-741. doi: 10.3934/dcdsb.2008.9.731 [7] Ta T.H. Trang, Vu N. Phat, Adly Samir. Finite-time stabilization and $H_\infty$ control of nonlinear delay systems via output feedback. Journal of Industrial & Management Optimization, 2016, 12 (1) : 303-315. doi: 10.3934/jimo.2016.12.303 [8] Richard H. Rand, Asok K. Sen. A numerical investigation of the dynamics of a system of two time-delay coupled relaxation oscillators. Communications on Pure & Applied Analysis, 2003, 2 (4) : 567-577. doi: 10.3934/cpaa.2003.2.567 [9] Fatiha Alabau-Boussouira, Vincent Perrollaz, Lionel Rosier. Finite-time stabilization of a network of strings. Mathematical Control & Related Fields, 2015, 5 (4) : 721-742. doi: 10.3934/mcrf.2015.5.721 [10] Linna Li, Changjun Yu, Ning Zhang, Yanqin Bai, Zhiyuan Gao. A time-scaling technique for time-delay switched systems. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 0-0. doi: 10.3934/dcdss.2020108 [11] Tingwen Huang, Guanrong Chen, Juergen Kurths. Synchronization of chaotic systems with time-varying coupling delays. Discrete & Continuous Dynamical Systems - B, 2011, 16 (4) : 1071-1082. doi: 10.3934/dcdsb.2011.16.1071 [12] B. Cantó, C. Coll, A. Herrero, E. Sánchez, N. Thome. Pole-assignment of discrete time-delay systems with symmetries. Discrete & Continuous Dynamical Systems - B, 2006, 6 (3) : 641-649. doi: 10.3934/dcdsb.2006.6.641 [13] Ming He, Xiaoyun Ma, Weijiang Zhang. Oscillation death in systems of oscillators with transferable coupling and time-delay. Discrete & Continuous Dynamical Systems - A, 2001, 7 (4) : 737-745. doi: 10.3934/dcds.2001.7.737 [14] Qinqin Chai, Ryan Loxton, Kok Lay Teo, Chunhua Yang. A unified parameter identification method for nonlinear time-delay systems. Journal of Industrial & Management Optimization, 2013, 9 (2) : 471-486. doi: 10.3934/jimo.2013.9.471 [15] Chongyang Liu, Meijia Han, Zhaohua Gong, Kok Lay Teo. Robust parameter estimation for constrained time-delay systems with inexact measurements. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019113 [16] Shu Dai, Dong Li, Kun Zhao. Finite-time quenching of competing species with constrained boundary evaporation. Discrete & Continuous Dynamical Systems - B, 2013, 18 (5) : 1275-1290. doi: 10.3934/dcdsb.2013.18.1275 [17] Grzegorz Karch, Kanako Suzuki, Jacek Zienkiewicz. Finite-time blowup of solutions to some activator-inhibitor systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (9) : 4997-5010. doi: 10.3934/dcds.2016016 [18] Emilija Bernackaitė, Jonas Šiaulys. The finite-time ruin probability for an inhomogeneous renewal risk model. Journal of Industrial & Management Optimization, 2017, 13 (1) : 207-222. doi: 10.3934/jimo.2016012 [19] Peter Giesl. Construction of a finite-time Lyapunov function by meshless collocation. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2387-2412. doi: 10.3934/dcdsb.2012.17.2387 [20] Khalid Addi, Samir Adly, Hassan Saoud. Finite-time Lyapunov stability analysis of evolution variational inequalities. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1023-1038. doi: 10.3934/dcds.2011.31.1023

Impact Factor: