Amplitude equation for a diffusion–reaction system in presence of complexing reaction with the activator species: the Brusselator model

For Brusselator diffusion–reaction model involving complex forming reaction with the activator species, an amplitude equation has been derived in the framework of a weakly nonlinear theory. Complexing reaction with the activator species strongly influences the time-dependent amplitudes such as in Hopf-wave bifurcations, whereas time-independent amplitudes such as in Turing—bifurcations, are independent of complexing reaction with the activator species. Complexing reaction arrests the arrival of Hopf—bifurcations and the domain of excitable non-oscillations such created may be used effectively for Turing-structure generation by inducing inhomogeneous perturbations of nonzero wavenumber mode. Any major complexing interaction with the activator species in a biological oscillatory network is bound to alter the domains of Hopf/Turing bifurcations affecting the course of physiological self-organization processes.