The existence of strange nonchaotic attractors in the quasiperiodically forced Ricker family
Gaolei Li, Yuan Yue, Denghui Li, Jianhua Xie, Celso Grebogi
Abstract
In this paper, the Ricker family (a population model) with quasiperiodic excitation is considered. The existence of strange nonchaotic attractors (SNAs) is analyzed in a co-dimension-2 parameter space by both theoretical and numerical methods. We prove that SNAs exist in a positive measure parameter set. The SNAs are nowhere differentiable (i.e., strange). We use numerical methods to identify the existence of SNAs in a larger parameter set. The nonchaotic property of SNAs is verified by evaluating the Lyapunov exponents, while the strange property is characterized by phase sensitivity and rational approximations. We also find that there is a transition region in a parameter plane in which SNAs alternate with chaotic attractors.