Complex dynamics and spatio-temporal patterns in a network of three distributed chemical reactors with periodical feed switching

Abstract

In this paper the dynamics of a periodically forced network of three catalytic reactors is studied. The reactors are modeled as distributed parameter systems with a Z3 � S 1 spatio-temporal symmetry. The symmetry property is induced by periodical forcing, and it forces the Poincaremap to be the third iterate of another non-stroboscopic map. This prop- erty is used to compute the bifurcation diagram of the periodic and multiperiodic regimes of the reactor network through the continuation of the corresponding fixed points of the non-stroboscopic map. Moreover, this property is used to determine the symmetry and multiplicity of the regimes by comparing the invariant sets of the Poincaremap with those of the non-stroboscopic map. As demonstrated in this paper, this is possible even for quasi-periodic and cha- otic regime. For symmetry and spatially distributed nature of the system, several complex symmetric and asymmetric spatio-temporal patterns corresponding to multiperiodic, quasi-periodic and chaotic regimes are found in a wide range of the bifurcation parameter. Symmetry breaking bifurcations, catastrophic transitions from periodic to quasi-periodic regimes, and different routes to chaotic regimes (Curry-Yorke, type I and III intermittencies and torus doubling cas- cade) are found and discussed. � 2005 Published by Elsevier Ltd.