How to Generate Chaos from Switching System : A Saddle Focus of Index 1 and Heteroclinic Loop-Based Approach
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-11-24
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
There exist two different types of equilibrium points in 3-D autonomous systems, named as saddle foci of index 1 and index 2, which are crucial for chaos generation.
Although saddle foci of index 2 have been usually applied for creating double-scroll or double-wing chaotic attractors, saddle foci of index 1 are further considered for chaos generation in this paper.
A novel approach for constructing chaotic systems is investigated by applying the switching control strategy and yielding a heteroclinic loop which connects two saddle foci of index 1.
A basic 3-D linear system with an arbitrary normal direction of the eigenplane, possessing a saddle focus of index 1 whose corresponding eigenvalues satisfy the Shil'nikov inequality, is first introduced.
Then a heteroclinic loop connecting two saddle foci of index 1 will be formed by applying the switching control strategy to the basic 3-D linear system.
The heteroclinic loop consists of an unstable manifold, a stable manifold, and a heteroclinic point.
Under the necessary conditions for forming the heteroclinic loop, the intended two-segmented piecewise linear system which exhibits the chaotic behavior in the sense of the Smale horseshoe can be finally constructed.
An illustrative example is given, confirming the effectiveness of the proposed method.
American Psychological Association (APA)
Bao, Fang& Yu, Simin. 2011. How to Generate Chaos from Switching System : A Saddle Focus of Index 1 and Heteroclinic Loop-Based Approach. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-496260
Modern Language Association (MLA)
Bao, Fang& Yu, Simin. How to Generate Chaos from Switching System : A Saddle Focus of Index 1 and Heteroclinic Loop-Based Approach. Mathematical Problems in Engineering No. 2011 (2011), pp.1-10.
https://search.emarefa.net/detail/BIM-496260
American Medical Association (AMA)
Bao, Fang& Yu, Simin. How to Generate Chaos from Switching System : A Saddle Focus of Index 1 and Heteroclinic Loop-Based Approach. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-496260
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-496260