Remark on positive entropy of a coupled lattice system related with Belusov-Zhabotinskii reaction

Authors：Li Risong^*; Zhao Yu

Source：Journal of Mathematical Chemistry, 2015, 53(10): 2115-2119.

DOI：10.1007/s10910-015-0538-y

• Coupled map lattice
• Positive topological entropy
• Devaney's chaos
• Chaos in the sense of Li-Yorke
• Tent map

In Garcia Guirao and Lampart (J Math Chem 48:159-164, 2010) presented a lattice dynamical system (LDS) stated by Kaneko (Phys Rev Lett 65:1391-1394, 1990) which is related to the Belusov-Zhabotinskii reaction. In this paper, we consider the following more general LDS:
x(n)(m+1) = (1 - epsilon) f(n) (x(n)(m)) + 1/2 epsilon [f(n) (x(n-1)(m)) - f(n) (x(n+1)(m))],
where m is discrete time index, n is lattice side index with system size L, is coupling constant and is a continuous selfmap on I for every . In particular, we prove that for zero coupling constant, if there is such that has positive topological entropy, then so does this coupled map lattice system. This result extends the existing one.

• Institution
  广东海洋大学