Perturbation-induced chaos in nonlinear Schrödinger equation with single source and its characterization

In this paper, we study the chaotic behavior of the nonlinear Schödinger equation with a single source under external perturbations. Based on Melnikov’s theorem, we prove the existence of chaos regardless of the complexity of the perturbation signals. Numerical simulations and electronic circuit experiments are also devised to verify this phenomenon. By investigating the Lyapunov spectrum and considering chaos suppression, we analyze the evolution properties of chaos excited by perturbations with different power and frequency richness. Results show that the noise-induced chaos possesses a larger positive Lyapunov exponent (LE), implying a stronger diversity, when the power of the perturbation signal increases. The corresponding chaos is also more difficult to be controlled and a larger control strength is needed to suppress the chaos. Moreover, it is noticed that, with the same signal power, the richer in frequency, the smaller the maximum LE. However, it is more difficult to control the induced chaos when the frequency of the perturbation signal is rich, yet the control strength remains more or less the same after certain level of frequency richness.