Antimonotonicity and chaotic dynamics in a fourth-order autonomous nonlinear electric circuit

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 characte ristic. Using the capacitances C-1 and C-2 as the control parameters, we ob serve the phenomenon of antimonotonicity and the formation of "bubbles" in the development of bifurcations, resulting typically in reverse period-doub ling sequences. We also find a crisis-induced intermittency, when the spira l attractor suddenly widens to a double-scroll attractor. We have plotted s everal bifurcation diagrams of reverse period-doubling sequences and comput ed the scaling parameter delta versus the control parameter C-2 for the dif ferent regimes, where bubbles evolve. Thus, besides the usual Feigenbaum co nstant delta --> delta(F) = 4.6692..., we also observe, in some cases, a co nvergence of delta to root delta(F), as expected from theoretical considera tions. Finally, by plotting a return map associated with one of the state v ariables, we demonstrate the strongly one-dimensional character of the dyna mics and discuss the dependence of this map on the parameters of the system .