摘要
A three-dimensional autonomous chaotic system is discussed in this paper. Some basic dynamical properties of the system, including phase portrait, Poincar′e map, power spectrum, Kaplan–Yorke dimension, Lyapunov exponent spectra, signal amplitude and topological horseshoe are studied theoretically and numerically. The main finding by analysis is that the signal amplitude can be modulated via controlling the coefficients of the linear term, cross-product term and squared term simultaneously or respectively, and the phase of x3 can be modulated by the product of the coefficients of the linear term and cross-product term. Furthermore, scaling chaotic attractors of this system are achieved by modified projective synchronization with an optimization-based linear coupling method, which is safer for secure communications than the existed synchronization scheme since the scaling factors can be regarded as the security encoding key.
基金
Supported by Hunan Provincial Natural Science Foundation of China under Grant No.2016JJ4036
University Natural Science Foundation of Jiangsu Province under Grant No.14KJB120007
the National Natural Science Foundation of China under Grant Nos.11504176and 11602084
