A Novel Fractional-Order System: Chaos, Hyperchaos and Applications to Linear Control

被引：17

作者：

Matouk, Ahmed Ezzat ^{[1
,2
,3
]}

机构：

[1] Majmaah Univ, Coll Sci Al Zulfi, Dept Math, Al Majmaah 11952, Saudi Arabia

[2] Majmaah Univ, Coll Engn, Al Majmaah 11952, Saudi Arabia

[3] Mansoura Higher Inst Engn & Technol, Damietta High Way, Mansourah, Egypt

来源：

JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS | 2021年 / 7卷 / 02期

关键词：

Fractional-order; Hopf bifurcation; Chaos; Hyperchaos; Linear control; DIFFERENTIAL-EQUATIONS; SYNCHRONIZATION; DYNAMICS; MODEL;

D O I：

10.22055/JACM.2020.35092.2561

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

Chaos and hyperchaos are generated from a new fractional-order system. Local stability of the system's three equilibria is analyzed when the fractional parameter belongs to (0,2]. According to Hopf bifurcation theory in fractional-order systems, approximations to the periodic solutions around the system's three equilibria are explored. Lyapunov exponents, Lyapunov spectrum and bifurcation diagrams are computed and chaotic (hyperchaotic) attractors are depicted. Furthermore, a linear control technique (LFGC) based on Lyapunov stability theory is implemented to derive the hyperchaotic states of the proposed system to its three equilibrium points. Numerical results are used to validate the theoretical results.

引用

页码：701 / 714

页数：14

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