Radially evolving spiral wave patterns in the Gierer-Meinhardt reaction-diffusion system

Spiral wave formation in spatially extended systems is a fascinating phenomenon that has garnered significant attention in reaction-diffusion systems. In this study, we explore the emergence of spiral wave-like patterns in the Gierer-Meinhardt reaction-diffusion model. By employing a multiple-time scale perturbation technique, we derive amplitude equations that reveal the conditions for spiral wave formation. Notably, our analysis shows that the amplitude of these spiral waves varies with the radial distance, introducing a distinctive feature to this pattern. Our theoretical predictions are further substantiated by numerical simulations, which confirm the emergence of spiral wave structures and validate the distinct radial dependence of their amplitude.