Stability analysis, chaos control of a fractional order chaotic chemical reactor system and its function projective synchronization with parametric uncertainties

被引：38

作者：

Yadav, Vijay K. ^{[1
]}

Das, Subir ^{[1
]}

Bhadauria, Beer Singh ^{[2
]}

Singh, Ashok K. ^{[3
]}

Srivastava, Mayank ^{[3
]}

机构：

[1] Indian Inst Technol BHU, Dept Math Sci, Varanasi 221005, Uttar Pradesh, India

[2] Babasaheb Bhimrao Ambedkar Univ, Dept Appl Math, Lucknow 226025, Uttar Pradesh, India

[3] Banaras Hindu Univ, Dept Math, Inst Sci, Varanasi 221005, Uttar Pradesh, India

来源：

CHINESE JOURNAL OF PHYSICS | 2017年 / 55卷 / 03期

关键词：

Fractional derivative; Chemical reactor system; Function projective synchronization; Luapunov stability theory; Nonlinear control method; SIMULATION; EQUATIONS; DYNAMICS; CIRCUIT;

D O I：

10.1016/j.cjph.2017.03.016

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this article, the stability analysis, chaos control and function projective synchronization between a fractional order chaotic chemical reactor system and a chaotic chemical reactor system with uncertain parameters are performed with the help of a new lemma for the Caputo derivative and the Lyapunov stability theory. Furthermore, when the parameters of the system are fixed, the lowest order for chaos to exist is determined. The nonlinear control method is used to achieve function projective synchronization and chaos control of considered chaotic chemical reactor system. Numerical simulations are carried out using the Adams-Bashforth Moulton method and the results are depicted through graphs. (C) 2017 The Physical Society of the Republic of China (Taiwan). Published by Elsevier B.V. All rights reserved.

引用

页码：594 / 605

页数：12

共 32 条

[1] Lyapunov functions for fractional order systems [J].

Aguila-Camacho, Norelys ;

Duarte-Mermoud, Manuel A. ;

Gallegos, Javier A. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (09) :2951-2957

[2]

[Anonymous], 2006, THEORY APPL FRACTION

[3] Complex dynamics and phase synchronization in spatially extended ecological systems [J].

Blasius, B ;

Huppert, A ;

Stone, L .

NATURE, 1999, 399 (6734) :354-359

[4] Function projective synchronization between two identical chaotic systems [J].

Chen, Yong ;

Li, Xin .

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2007, 18 (05) :883-888

[5] On certain exact solutions of diffusive predator-prey system of fractional order [J].

Choi, Jin Hyuk ;

Kim, Hyunsoo ;

Sakthivel, Rathinasamy .

CHINESE JOURNAL OF PHYSICS, 2016, 54 (01) :135-146

[6] CIRCUIT IMPLEMENTATION OF SYNCHRONIZED CHAOS WITH APPLICATIONS TO COMMUNICATIONS [J].

CUOMO, KM ;

OPPENHEIM, AV .

PHYSICAL REVIEW LETTERS, 1993, 71 (01) :65-68

[7] Multi-order fractional differential equations and their numerical solution [J].

Diethelm, K ;

Ford, NJ .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 154 (03) :621-640

[8] Detailed error analysis for a fractional Adams method [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD .

NUMERICAL ALGORITHMS, 2004, 36 (01) :31-52

[9] Modified function projective synchronization of chaotic system [J].

Du, Hongyue ;

Zeng, Qingshuang ;

Wang, Changhong .

CHAOS SOLITONS & FRACTALS, 2009, 42 (04) :2399-2404

[10] THERMODYNAMIC FLUCTUATIONS AND CHEMICAL CHAOS IN A WELL-STIRRED REACTOR - A MASTER EQUATION ANALYSIS [J].

GEYSERMANS, P ;

NICOLIS, G .

JOURNAL OF CHEMICAL PHYSICS, 1993, 99 (11) :8964-8969

← 1 2 3 4 →