Abstract
This paper investigates a class of linear continuous-time switching systems and proposes a new approach to generate chaos by designing a hybrid switching rule. First, a computational formula for Lyapunov exponents is derived by extending the definition of Lyapunov exponent for continuous-time autonomous systems to that of a class of linear continuous-time switching systems. Then, a novel switching rule is proposed to gain global boundedness property as well as the required placement of Lyapunov exponents for chaos. A numerical example is given to illustrate the chaotic dynamic behavior of the generated system. The Lyapunov dimension of the system in the example is calculated and the corresponding bifurcation diagram and Lyapunov spectra are sketched, which, together with other phase portraits, clearly verify the validity of the main result.
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