TY - JOUR
T1 - Chaotifying continuous-time nonlinear autonomous systems
AU - Yu, Simin
AU - Chen, Guanrong
PY - 2012/9
Y1 - 2012/9
N2 - Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e. being globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible and unified chaotification method for designing a general chaotic continuous-time autonomous nonlinear system. For a system consisting of a linear and a nonlinear subsystems, chaotification is achieved using separation of state variables, which decomposes the system into two open-loop subsystems interacting through mutual feedback resulting in an overall closed-loop nonlinear feedback system. Under the condition that the nonlinear feedback control output is uniformly bounded where the nonlinear function is of bounded-input/bounded-output, it is proved that the resulting system is chaotic in the sense of being globally bounded with a required placement of Lyapunov exponents. Several numerical examples are given to verify the effectiveness of the theoretical design. Since linear systems are special cases of nonlinear systems, the new method is also applicable to linear systems in general. © 2012 World Scientific Publishing Company.
AB - Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e. being globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible and unified chaotification method for designing a general chaotic continuous-time autonomous nonlinear system. For a system consisting of a linear and a nonlinear subsystems, chaotification is achieved using separation of state variables, which decomposes the system into two open-loop subsystems interacting through mutual feedback resulting in an overall closed-loop nonlinear feedback system. Under the condition that the nonlinear feedback control output is uniformly bounded where the nonlinear function is of bounded-input/bounded-output, it is proved that the resulting system is chaotic in the sense of being globally bounded with a required placement of Lyapunov exponents. Several numerical examples are given to verify the effectiveness of the theoretical design. Since linear systems are special cases of nonlinear systems, the new method is also applicable to linear systems in general. © 2012 World Scientific Publishing Company.
KW - Chaos
KW - Chaotification
KW - Continuous-time system
KW - Global boundedness
KW - Lyapunov exponent
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84867523981&origin=recordpage
U2 - 10.1142/S021812741250232X
DO - 10.1142/S021812741250232X
M3 - RGC 21 - Publication in refereed journal
VL - 22
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
SN - 0218-1274
IS - 9
M1 - 1250232
ER -