Existence of Chaos, dynamical behaviour with fractional order derivatives and modified adaptive function projective synchronization with uncertain parameters of a chaotic system

被引：2

作者：

Agrawal, S. K. ^{[1
]}

Vishal, K. ^{[2
]}

机构：

[1] Bharati Vidyapeeths Coll Engn, Dept Appl Sci, New Delhi 110063, India

[2] NIIT Univ, Dept Math & Basic Sci, Neemrana 301705, Rajasthan, India

来源：

OPTIK | 2017年 / 131卷

关键词：

Chaos; Largest Lyapunov Exponent (LLE); Fractional derivative; Duffing-Van der Pol system; Chaos control; Feedback control; Modified adaptive function projective synchronization; POL SYSTEMS; MATHIEU-VAN; DIFFERENTIAL-EQUATIONS; HYPERCHAOTIC SYSTEMS; STABILITY; DESIGN; CONTROLLER;

D O I：

10.1016/j.ijleo.2016.11.070

中图分类号：

O43 [光学];

学科分类号：

070207 ; 0803 ;

摘要：

In this article, the authors have studied dynamics of Duffing-Van der Pol system with fractional order derivative and found the existence of chaos. The main contribution of this effort is implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf's algorithm. The conditions for chaos control based on fractional Routh-Hurwitz stability conditions and feedback control are obtained. Also synchronization between fractional order chaotic system and controlled fractional order Duffing-Van tier Pol system using modified adaptive function projective synchronization method for different scaling matrix has been obtained. Numerical simulation results which are carried out using Adams-Bashforth-Moulton method show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order systems. (C) 2016 Elsevier GmbH. All rights reserved.

引用

页码：89 / 103

页数：15

共 33 条

[1] Function projective synchronization between four dimensional chaotic systems with uncertain parameters using modified adaptive control method
Agrawal, S. K.
Das, S.
[J]. JOURNAL OF PROCESS CONTROL, 2014, 24 (05) : 517 - 530
[2] A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters
Agrawal, S. K.
Das, S.
[J]. NONLINEAR DYNAMICS, 2013, 73 (1-2) : 907 - 919
[3] Projective synchronization between different fractional-order hyperchaotic systems with uncertain parameters using proposed modified adaptive projective synchronization technique
Agrawal, Saurabh K.
Das, Subir
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2014, 37 (14) : 2164 - 2176
[4] Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models
Ahmed, E.
El-Sayed, A. M. A.
El-Saka, H. A. A.
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (01) : 542 - 553
[5] On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems
Ahmed, E.
El-Sayed, A. M. A.
El-Saka, Hala A. A.
[J]. PHYSICS LETTERS A, 2006, 358 (01) : 1 - 4
[6] Synchronization of an uncertain unified chaotic system via adaptive control
Chen, SH
Lü, JH
[J]. CHAOS SOLITONS & FRACTALS, 2002, 14 (04) : 643 - 647
[7] Adaptive synchronization of different chaotic systems with fully unknown parameters
Chen, Xiaoyun
Lu, Jianfeng
[J]. PHYSICS LETTERS A, 2007, 364 (02) : 123 - 128
[8] A new 3D chaotic system: Dynamical analysis, electronic circuit design, active control synchronization and chaotic masking communication application
Cicek, S.
Ferikoglu, A.
Pehlivan, I.
[J]. OPTIK, 2016, 127 (08): : 4024 - 4030
[9] Partial chaos suppression in a fractional order macroeconomic model
David, S. A.
Machado, J. A. T.
Quintino, D. D.
Balthazar, J. M.
[J]. MATHEMATICS AND COMPUTERS IN SIMULATION, 2016, 122 : 55 - 68
[10] Multi-order fractional differential equations and their numerical solution
Diethelm, K
Ford, NJ
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2004, 154 (03) : 621 - 640

← 1 2 3 4 →