期刊
NONLINEAR DYNAMICS
卷 81, 期 1-2, 页码 227-237出版社
SPRINGER
DOI: 10.1007/s11071-015-1984-6
关键词
Piecewise continuous function; Fractional-order system; Piecewise continuous system of fractional order; Lyapunov exponent; Chaotic system
In this paper, we prove that a class of piecewise continuous autonomous systems of fractional order has well-defined Lyapunov exponents. To do so, based on some known results from differential inclusions of integer order and fractional order, as well as differential equations with discontinuous right-hand sides, the corresponding discontinuous initial value problem is approximated by a continuous one with fractional order. Then, the Lyapunov exponents are numerically determined using, for example, Wolf's algorithm. Three examples of piecewise continuous chaotic systems of fractional order are simulated and analyzed: Sprott's system, Chen's system, and Simizu-Morioka's system.
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