Mixed-mode oscillations and chaotic solutions of jerk (Newtonian) equations

[摘要] 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 firstorder 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 = 0 for a constant mass m and specially designed nonlinear force function F (x, x', tau). 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. (C) 2013 Elsevier B.V. All rights reserved.

[发布日期] 2014-05-15

[效力级别]  Proceedings Paper

[关键词] Mixed-mode oscillations;Jerk equations;Newtonian oscillations;Bifurcations;Chaos