In this paper we study the dynamics of a fourth-order autonomous nonlinear electric circuit with two active elements, one linear negative conductance and one nonlinear resistor with a symmetrical piecewise-linear v-i characteristic. Using the capacitances C1 and C2 as the control parameters, we observe the phenomenon of antimonotonicity and the formation of "bubbles" in the development of bifurcations, resulting typically in reverse period-doubling sequences. We also find a crisis-induced intermittency, when the spiral attractor suddenly widens to a double-scroll attractor. We have plotted several bifurcation diagrams of reverse period-doubling sequences and computed the scaling parameter δ versus the control parameter C2 for the different regimes, where bubbles evolve. Thus, besides the usual Feigenbaum constant δ → δF = 4.6692 ..., we also observe, in some cases, a convergence of δ to √δF, as expected from theoretical considerations. Finally, by plotting a return map associated with one of the state variables, we demonstrate the strongly one-dimensional character of the dynamics and discuss the dependence of this map on the parameters of the system.
|Number of pages||13|
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|Publication status||Published - Aug 2000|
ASJC Scopus subject areas
- Modelling and Simulation
- Engineering (miscellaneous)
- Applied Mathematics