Amplitude-modulated spiral waves arising from a secondary Hopf bifurcation in mixed-mode oscillatory media

Herein we communicate on the spatial temporal dynamics of a diffusively-coupled medium of Rössler oscillators under mixed-mode regime. The secondary Hopf bifurcation, resulting from coupling between mixed-mode oscillations and diffusion was found to produce amplitude-modulated spiral waves, including overtarget waves and superspiral waves on the basic spiral waves. The Poincaré return maps and Fourier spectra were used to analyze the different spatiotemporal structures. The diffusion-induced torus oscillations form the dynamical basis for all kinds of superposition waves in autonomous reaction–diffusion systems.