Oscillatory chemical reactions: the Tomita-Kitahara model

Biological clocks share with excitable membrane (nerve, muscle) the requirement that the chemical systems that underlie them have unstable steady states, and hence are capable of limit-cycle oscillations. A particularly simple model of a chemical oscillator is discussed, especially with reference to the reverse reaction, which tends to damp the oscillations. For thermodynamic reasons (entropy production) reversibility can not, however, be neglected. The steady state, even when stable, does not minimize the dissipation function. Computer studies show the response to sinusoidal variation of the rate constant governing the autocatalytic step.