Oregonator-Type Kinetics

For kinetic schemes with a structure similar to the Oregonator model, i.e., f2iPn-, Pm) = 0, the expressions for the instability thresholds, (13.175) and (13.176), and for the instability conditions, (13.177) and (13.178), simplify to 

If the coupling is via the inhibitor only, = 0, then no Hopf instability can occur. The condition for a stationary instability to occur is given by 

For kinetic schemes that like the Oregonator model and pure activator-inhibitor schemes in general have /21 0, a stationary instability can occur only if c and F have opposite signs, i.e., if the coupling is inhibitory. The uniform steady state of an array of photochemically coupled Oregonator undergoes a stationary instability at 

If the coupling is via the activator only, c = 0, the thresholds for the stationary and for the oscillatory instability are given by 

---