Chaoticity of some chemical attractors: a computer assisted proof

Abstract

In this paper we study dynamics of two chemical attractors. By means of computer assisted proof, we show that these chemical attractors are chaotic in terms of positive entropy. We prove that the fourth power of the Poincaré map derived from one chemical attractor and the second power of the Poincaré map derived from the other chemical attractor are semi-conjugate to the 2-shift map, therefore the entropies of the two Poincaré maps are not less than ${{1}\over {4}}$log 2 and ${{1}\over {2}}$log 2, respectively. The positivity of entropies of these two maps shows that the corresponding attractors are chaotic.