ANALYSIS AND DESIGN OF ANTI-CONTROLLED HIGHER-DIMENSIONAL HYPERCHAOTIC SYSTEMS VIA LYAPUNOV-EXPONENT GENERATING ALGORITHMS

Jianbin He; Simin Yu; Jianping Cai

doi:10.11948/2016075

2016 Volume 6 Issue 4

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Article navigation > Journal of Applied Analysis & Computation > 2016 > 6(4): 1135-1151

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Jianbin He, Simin Yu, Jianping Cai. ANALYSIS AND DESIGN OF ANTI-CONTROLLED HIGHER-DIMENSIONAL HYPERCHAOTIC SYSTEMS VIA LYAPUNOV-EXPONENT GENERATING ALGORITHMS[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 1135-1151. doi: 10.11948/2016075

Citation:

Jianbin He, Simin Yu, Jianping Cai. ANALYSIS AND DESIGN OF ANTI-CONTROLLED HIGHER-DIMENSIONAL HYPERCHAOTIC SYSTEMS VIA LYAPUNOV-EXPONENT GENERATING ALGORITHMS[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 1135-1151. doi: 10.11948/2016075

ANALYSIS AND DESIGN OF ANTI-CONTROLLED HIGHER-DIMENSIONAL HYPERCHAOTIC SYSTEMS VIA LYAPUNOV-EXPONENT GENERATING ALGORITHMS

1 College of Automation, Guangdong University of Technology, Guangzhou 510006, China;
2 College of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China

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Abstract

Abstract

Based on Lyapunov-exponent generation and the Gram-Schimdt orthogonalization, analysis and design of some anti-controlled higher-dimensional hyperchaotic systems are investigated in this paper. First, some theoretical results for Lyapunov-exponent generating algorithms are proposed. Then, the relationship between the number of Lyapunov exponents and the number of positive real parts of the eigenvalues of the Jacobi matrix is qualitatively described and analyzed. By configuring as many as possible positive real parts of the Jacobian eigenvalues, a simple anti-controller of the form b sin(σx) for higher-dimensional linear systems is designed, so that the controlled systems can be hyperchaotic with multiple positive Lyapunov exponents. Utilizing the above property, one can resolve the positive Lyapunov exponents allocation problem by purposefully designing the number of positive real parts of the corresponding eigenvalues. Two examples of such anti-controlled higherdimensional hyperchaotic systems are given for demonstration.
- Lyapunov exponent /
- QR-factorization /
- eigenvalue of Jacobi matrix /
- chaos anti-control
MSC: 34D08;37M25;65P20

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References

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