一个四翼混沌吸引子

在新的四维混沌系统中数值观察到四翼混沌吸引子，然而，通过进一步分析发现，该四翼吸引子并非真实的，实际上它是上、下两个共存的双翼混沌吸引子，他们各自有独立的混沌吸引域，由于其位置靠得太近和数值误差产生的一种假象.通过引入一个线性状态反馈控制项，系统的一些相似性被破坏，受控系统能产生穿越上下吸引域界限的对角双翼混沌吸引子，进一步，随着动力学模态的演化，上下混沌吸引子与对角混沌吸引子融合成一个真正的四翼混沌吸引子.最后，通过比较该四翼混沌吸引子的系统、Lorenz系统、Chua氏电路等混沌信号的频谱发现，四翼混沌吸引子的系统信号具有极宽的频谱带宽，该特性在通讯加密等工程应用中具有重要价值. 关键词： 四维混沌系统 双翼吸引子 四翼吸引子 频谱分析

On a four-winged chaotic attractor

A four-winged chaotic attractor was first observed numerically in a new 4-dimensional system. However, it was found to be a numerical artifact upon further analysis. It actually consists of two (upper and lower) coexisting double-wing chaotic attractors with domains of attraction independent of each other. The reason leading to the confusion is that both double-wing attractors are arbitrarily close to each other so as to cause a numerical error as well as a misunderstanding. By adding a simple linear state feedback term to the system, some similaritics of the system are destroyed, then the controlled system is able to generate diagonal double chaotic attractor which can cross the boundary between the upper and lower attractive domains. With the evolution of dynamical modes, the upper and the lower double-wing chaotic attractors as well as diagonal chaotic attractor are merged into a true four-winged chaotic attractor. At last, the frequency spectrum analysis shows that the four-winged chaotic attractor has extremely wide frequency bandwidth compared with that of the Lorenz system and Chua circuit, which is important in practical applications in communication encryption etc.