TY - JOUR
T1 - Constructing hyperchaotic systems at will
AU - Shen, Chaowen
AU - Yu, Simin
AU - Lü, Jinhu
AU - Chen, Guanrong
PY - 2015/12
Y1 - 2015/12
N2 - Over the last two decades, chaotification has received increasing attention from various communities of science and engineering. This paper aims at developing a unified chaotification framework for generating desired higher-dimensional dissipative hyperchaotic systems by using a single-parameter controller. The main idea is to use a block diagonal matrix in the design of the nominal system, so as to construct a desired hyperchaotic system. Specifically, the proposed scheme is to assign desired closed-loop poles to the controlled system, allocating the corresponding numbers of eigenvalues with positive real parts at two types of saddle-focus equilibria. For the non-degenerate case, the number of positive Lyapunov exponents of the controlled system is given by the largest number of positive Lyapunov exponents of the desired hyperchaotic system. Two representative examples are given to illustrate and verify the proposed design method. Finally, the digital signal processor is employed to implement the above 10-dimensional hyperchaotic systems, and the experimental observation is also given.
AB - Over the last two decades, chaotification has received increasing attention from various communities of science and engineering. This paper aims at developing a unified chaotification framework for generating desired higher-dimensional dissipative hyperchaotic systems by using a single-parameter controller. The main idea is to use a block diagonal matrix in the design of the nominal system, so as to construct a desired hyperchaotic system. Specifically, the proposed scheme is to assign desired closed-loop poles to the controlled system, allocating the corresponding numbers of eigenvalues with positive real parts at two types of saddle-focus equilibria. For the non-degenerate case, the number of positive Lyapunov exponents of the controlled system is given by the largest number of positive Lyapunov exponents of the desired hyperchaotic system. Two representative examples are given to illustrate and verify the proposed design method. Finally, the digital signal processor is employed to implement the above 10-dimensional hyperchaotic systems, and the experimental observation is also given.
KW - chaotification
KW - closed-loop poles assignment
KW - DSP realization
KW - hyperchaotic system
KW - Lyapunov exponents allocation
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84957845026&origin=recordpage
U2 - 10.1002/cta.2062
DO - 10.1002/cta.2062
M3 - 21_Publication in refereed journal
VL - 43
SP - 2039
EP - 2056
JO - International Journal of Circuit Theory and Applications
JF - International Journal of Circuit Theory and Applications
SN - 0098-9886
IS - 12
ER -