Controlling Spatiotemporal Chaos by Pinning Method in Two-Dimensional Coupled Map Lattices

Abstract

Spatiotemporal chaos in two-dimensional logistic coupled map lattices is controlled by a pinning method, which is a partial-site local control scheme. The effectiveness of the control depends not only on the pinning density, but also on the pinning distribution pattern. The control is more successful with increase of the pinning density, and more effective with use of an optimal pinning pattern which sets more pinning sites around a no-pinning site.

Spatio-Temporal Chaos and Vacuum Fluctuations of Quantized Fields

“…Generally, the spectrum of possibilities of spatio-temporal structures that can be generated by coupled map lattices is extremely rich and has been extensively studied in the literature, the emphasis being on the bifurcation structure [Bunimovich et al (1996), Just (1995, Amritkar et al (1993)] [Gade et al (1993), Amritkar et al (1991), Pikovsky et al (1991)], Liapunov exponents [Yang et al (1996), Torcini et al (1997b), Kaneko (1986b)] [Isola et al (1990)], traveling waves [Carretero-González (1997)] [He et al (1997)], phase transition-like phenomena [Grassberger et al (1991), Cuche et al (1997), Blank (1997), Marcq et al (1996)] [Boldrighini et al (1995), Keller et al (1992a), Houlrik et al (1992)] [Miller et al (1993), Gielis et al (2000)], the existence of smooth invariant measures [Baladi et al (1998), Jiang et al (1998a), ] [Mackey et al (1995)], synchronization [Lemaitre et al (1999)] [Bagnoli et al (1999), de San Roman et al (1998), Jiang et al (1998b)] [Wang et al (1998), Ding et al (1997)], control [Gade (1998)] [Egolf et al (1998), Parekh et al (1998), Mondragon et al (1997)] [Ohishi et al (1995)] and many other properties. Applications for coupled map systems have been pointed out for various subjects, among them hydrodynamic turbulence [Beck (1994), Hilgers et al (1997b), …”