کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4638984 | 1632029 | 2014 | 11 صفحه PDF | دانلود رایگان |
We analyze jerk equations (third-order ODEs) resulting from an underlying prototypical model of mixed-mode oscillations and propose their circuit realizations in this paper. The scalar ODEs and their corresponding circuit realizations are obtained from a system of first-order ODEs with one nonlinearity (third-degree polynomial). One of the jerk equations is Newtonian as it is obtained by computing the time-derivative of the second Newton’s law x″−F/m=0x″−F/m=0 for a constant mass mm and specially designed nonlinear force function F(x,x′,τ)F(x,x′,τ). The second jerk equation is non-Newtonian. The two circuits are op-amp RC circuits with interesting dynamical properties, including the mixed-mode and chaotic oscillations. The mixed-mode oscillations follow the rules of Farey arithmetic and the circuits’ dynamics is of a fractal nature.
Journal: Journal of Computational and Applied Mathematics - Volume 262, 15 May 2014, Pages 373–383