Chein-Shan Liu1
CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.4, pp. 375-407, 2014, DOI:10.3970/cmes.2014.098.375
Abstract In this paper we study the nonlinear dynamical system x·=f(x,t) from a newly developed theory, viewing the time-varying function of sign(||f||2||x||2− 2(f·x)2) = −sign(cos 2θ) as a key factor, where θ is the intersection angle between x and f. It together with sign(cos θ) can reveal the complexity of nonlinear Duffing oscillator and a quadratic ship rolling oscillator. The barcode is formed by plotting sign(||f||2||x||2− 2(f·x)2) with respect to time. We analyze the barcode to point out the bifurcation of subharmonic motions and the range of chaos in the parameter space. The bifurcation diagram obtained by plotting the percentage… More >
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