Theoretical Models of Chronotherapy: I. Periodic Perturbations in Oscillating Chemical Reactions

Abstract

Dynamics resulting from periodic perturbations in oscillating chemical reaction, as theoretical models of chronotherapy techniques are studied. Replication reactions and fluctuations take place in these models giving rise to new species with autocatalitic properties. Oscillating chemical reaction models due to Hanusse (H) with three intermediaries and Bourceanu (E1, E2, E3 ) with four, five and six intermediaries, respectively, are taken for this study and are manipulated numerically using a Gear algorithm. The bifurcation diagrams are obtained applying non-linear dynamic techniques, such as, power spectrum, stroboscopic method, Lyapunov exponents and correlation dimension D 2. The dynamics of Hanusse and Bourceanu perturbed models are very similar. The main dynamic behaviours observed after perturbation are quasiperiodicity, entrainment, some Arnold tongues and situations without chemical meaning. Chaos is not observed. This study contributes to understand theoretical and practical aspects of the chronotherapy techniques.