标题：Regular Nonchaotic Attractors with Positive Plural
作者机构：[Zhang, Xu] Shandong Univ, Dept Math, Weihai 264209, Shandong, Peoples R China.
通讯作者地址：[Zhang, X]Shandong Univ, Dept Math, Weihai 264209, Shandong, Peoples R China.
来源：INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
关键词：Attractor; nonautonomous; nonchaotic; positive plural; regular
摘要：The study of the strange nonchaotic attractors is an interesting topic, where the dynamics are neither regular nor chaotic (the word chaotic means the positive Lyapunov exponents), and the shape of the attractors has complicated geometry structure, or fractal structure. It is found that in a class of planar first-order nonautonomous systems, it is possible that there exist attractors, where the shape of the attractors is regular, the orbits are transitive on the attractors, and the dynamics are not chaotic. We call this type of attractors as regular nonchaotic attractors with positive plural, which are different from the strange nonchaotic attractors, attracting fixed points, or attracting periodic orbits. Several examples with computer simulations are given. The first two examples have annulus-shaped attractors. Another two examples have disk-shaped attractors. The last two examples with externally driven terms at two incommensurate frequencies have regular nonchaotic attractors with positive plural, implying that the existence of externally driven terms at two incommensurate frequencies might not be the sufficient condition to guarantee that the system has strange nonchaotic attractors.