Paper Info
Title
Constructing Higher-Dimensional Nondegenerate Hyperchaotic Systems With Multiple Controllers
Abstract
This paper proposes a new approach for constructing higher-dimensional nondegenerate hyperchaotic system with multiple controllers. Here, the so-called higher-dimensional nondegenerate hyperchaotic system means that it can be provided with a maximum number of positive Lyapunov exponents, which has been an open problem for research in recent years. The details of design are given by three steps as follows: (i) Design an n-dimensional nominal matrix and similarity transformation matrix, and get an asymptotic stable nominal system; (ii) Add a master controller for the nominal matrix and get the controlled system. Then, find suitable control positions such that the controlled system satisfies the average eigenvalue criterion, i.e. the number of average eigenvalues with positive real parts of all Jacobi matrices over a given period of time is equal to (n - 2), and the maximum value of average eigenvalues with positive real parts is greater than a given threshold T-h; (iii) Add nonmaster controllers, and the control positions are fixed and parameters are given in advance. So it can generate nondegenerate hyperchaotic systems with (n - 2) positive Lyapunov exponents. Finally, two typical examples are given to show the feasibility and effectiveness of the proposed method.
Year
DOI
Venue
2017
10.1142/S0218127417501462
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Keywords
Field
DocType
Chaos anti-control, nondegenerate hyperchaotic system, multiple controllers, positive Lyapunov exponent
Control theory,Matrix similarity,Open problem,Matrix (mathematics),Control theory,Degeneracy (mathematics),Mathematics,Eigenvalues and eigenvectors,Lyapunov exponent
Journal
Volume
Issue
ISSN
27
9
0218-1274
Citations 
PageRank 
References 
2
0.41
14
Authors
3
Name
Order
Citations
PageRank
Jianbin He120.41
Simin Yu232025.49
Lv Jinhu32906244.29