Well-behaved dynamics in a dissipative nonideal periodically kicked rotator

Well-behaved dynamical properties are found in a dissipative kicked rotator subjected to a periodic string of asymmetric pulses of finite amplitude and width. The stability boundaries of the equilibrium are determined to arbitrary approximation for trigonometric pulses by means of circular harmonic balance, and to first approximation for general elliptic pulses by means of an elliptic harmonic balance method. The bifurcation behavior at the stability boundaries is determined numerically. We show how the extension of the instability region of the equilibrium in pulse parameter space reaches a maximum as the pulse width is varied. We also characterize the dependence of the mean duration of the transients to the equilibrium on the pulse width. The evolution of the basins of attraction of chaotic attractors when solely the pulse width is varied is characterized numerically. Finally, we show that the order-chaos route when solely the width of the pulses is altered appears to be especially rich, including different types of crises. The mechanism underlying these reshaping-induced crises is discussed with the aid of a two-dimensional map.