where

is the conversion of reactant

,

is the reactor temperature,

is the Damköhler number,

is the inverse activation energy,

is the heat of reaction,

is the heat transfer coefficient,

is the coolant forcing function,

is the average coolant temperature during forcing,

is the forcing amplitude,

is the forcing frequency, and

is time. The following parameters are considered:

,

,

,

,

, with

. The unforced system,

, has a single oscillatory state; increasing the amplitude of the forcing function results in quasi-periodic behavior, followed by a sequence of period-doubling bifurcations leading to chaos. Furthermore, bistability can occur where both states are periodic or one state is periodic and the other chaotic.