The Flow of a DAE near a Singular Equilibrium
SIAM Journal on Matrix Analysis and Applications
Chaos and Time-Series Analysis
Chaos and Time-Series Analysis
Simple autonomous chaotic circuits
IEEE Transactions on Circuits and Systems II: Express Briefs
Hi-index | 7.29 |
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=0 for a constant mass m and specially designed nonlinear force function F(x,x^',@t). 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.