Complex Dynamics and Chaos in a Hybrid System Modeling a Controlled Reverse Flow Reactor

In this work some complex behaviors of a controlled reverse flow reactor is presented. The control system introduces discrete events making the model an infinite dimensional hybrid system. The study is conducted through continuation techniques and brute force numerical simulations. Together with standard bifurcations like pitchfork, saddle-node and Neimark–Sacker, varying the set-point parameter of the controller, several novel aspects are singled out: an unusual sequence of period-adding bifurcation phenomena, a new route to chaos and the coexistence of Zeno states with quasi-periodic and chaotic regimes. The period-adding phenomena dictate the transition between symmetric and asymmetric multiperiodic regimes and a simple rule for the occurrence of symmetry breaking and recovery is found. The new route to chaos is a transition from a quasi-periodic regime to chaos due to the presence of Zeno phenomena, typical of hybrid systems. The chaos is characterized by Zeno-like oscillations.