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

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×S1 spatio-temporal symmetry. The symmetry property is induced by periodical forcing, and it forces the Poincaré map to be the third iterate of another non-stroboscopic map. This property 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 Poincarè map with those of the non-stroboscopic map. As demonstrated in this paper, this is possible even for quasi-periodic and chaotic 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 cascade) are found and discussed.