Mixed-Mode Oscillations in the Nonisothermal Autocatalator

The internal coupling of chemical and thermal feedback processes is investigated through a non-isothermal autocatalator model. The isothermal oscillatory scheme is augmented to include an exothermic “termination” step and a temperature-dependent initiation: P → A (rate = k₀(T)p); A + 2B → 3B (rate = k₁ab2); A → B (rate = k₃a); B → C+ heat (rate = k₂b). The pool chemical approximation is applied to reactant P. Multiple stationary states exist for all parameter values and complex dynamic behaviour is also found over wide ranges of these parameters. Path following techniques are used to follow the periodic solutions and to find bifurcations such as period doubling cascades leading to chaos. Other types of complex dynamics such as mixed mode oscillations are categorised, although we find no quasiperiodic behaviour in the model. This gives rise to the belief that the mixed mode oscillations found, do not stem from phase locking on a torus in this instance.