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 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 → δ_F = 4.6692…, we also observe, in some cases, a convergence of δ to , 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.