Predictability of the onset of spiking and bursting in complex chemical reactions

Abstract

For three complex chemical reactions displaying intricate dynamics, we assess the effectiveness of a recently proposed quantitative method to forecast bursting and large spikes, i.e. extreme events. Specifically, we consider predicting extreme events in (i) a copper dissolution model where Bassett and Hudson experimentally observed homoclinic (Shilnikov) chaos, (ii) a model derived from the mass action law of chemical kinetics, and (iii) an autocatalator model. For these systems, we describe how the alignment of Lyapunov vectors can be used to predict the imminence of large-amplitude events and the onset of complex dynamics in chaotic time-series of observables.