Reactive oxygen species (ROS) and peroxidase-oxidase (PO) reactions are Janus-faced contributors to cellular metabolism. At low concentrations, reactive oxygen species serve as signaling molecules; at high concentrations, as destroyers of proteins, lipids and DNA. Correspondingly, PO reactions are both sources and consumers of ROS. In the present paper, we study a well-tested model of the PO reaction based on horseradish peroxidase chemistry. Our principal predictions are these: 1. Under hypoxia, the PO reaction can emit pulses of hydrogen peroxide at apparently arbitrarily long intervals. 2. For a wide range of input rates, continuing infusions of ROS are transduced into bounded dynamics. 3. The response to ROS input is hysteretic. 4. With sufficient input, regulatory capacity is exceeded and hydrogen peroxide, but not superoxide, accumulates. These results are discussed with regard to the episodic nature of neuro developmental and neurodegenerative diseases that have been linked to oxidative stress and to downstream interactions that may result in positive feedback and pathology of increasing severity.