The principal measure and distributional -chaos of a coupled lattice system with coupling constant related with Belusov-Zhabotinskii reaction

作者：Li Risong^*; Huang Fu; Zhao Yu; Chen Zengxiong; Huang Cunyou

来源：Journal of Mathematical Chemistry, 2013, 51(7): 1712-1719.

DOI：10.1007/s10910-013-0174-3

• Coupled map lattice
• Distributional (p
• q)-chaos
• Principal measure
• Devaney's chaos
• Chaos in the sense of Li-Yorke
• Tent map

We consider the following system coming from a lattice dynamical system stated by Kaneko (Phys Rev Lett, 65:1391-1394, 1990) which is related to the Belusov-Zhabotinskii reaction: where is discrete time index, is lattice side index with system size (i.e., ), is coupling constant, and is the unimodal map on (i.e., , and has unique critical point with and ). In this paper, we prove that for coupling constant , this CML (Coupled Map Lattice) system is distributionally -chaotic for any with , and that its principal measure is not less than . Consequently, the principal measure of this system is not less than for coupling constant and the tent map defined by . So, our results complement the results of Wu and Zhu (J Math Chem, 50:2439-2445, 2012).

• 单位
  广东海洋大学