Lengyel-Epstein-Type Kinetics

If the coupling is via the inhibitor only, = 0, for kinetic schemes with a strucmre similar to the Lengyel-Epstein model, i.e., fiiPu, Pv) = —const/2(Pu P ) then the instability threshold expressions simplify  

Equation (13.163) implies that an increase in the light intensity leads to a decrease in the production rate of the activator. Therefore = 1 corresponds again to inhibitory coupling and c = — 1 to activatory coupling. 

The uniform steady state of Q undergoes a Hopf instability only if c G is negative, i.e., for activatory coupling. The stationary instability can only occur if 

The uniform steady state undergoes a stationary instability for inhibitory coupling at 

If the coupling occurs via the activator only, = 0, then the instability conditions read 

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