Programmable Spiral Wave Dynamics: Instability Cascades Driven by Temporal Modulation in a Reaction-Diffusion System.

Spiral waves are iconic structures and are striking hallmarks of self-organization in chemical and biological systems. While their instabilities under spatial inhomogeneities have been widely studied, the response of spirals to temporal modulations particularly near the Turing threshold yet away from Hopf bifurcation, remains underexplored. In this study, we reveal how periodic forcing of a kinetic parameter in the Chlorine Dioxide-Iodine-Malonic Acid model unlocks a diverse and tunable landscape of spiral wave instabilities in a regime that is spatially stable yet temporally unstable. Starting from a robust single-arm spiral, we observe a cascade of modulation-induced phenomena: breathing spirals, core drift, spiral breakup and turbulence, as well as transitions to oscillating clusters, Ising-front-like patterns, and spatially uniform bulk oscillations. Remarkably, we identify spiral regeneration with altered arm width and chirality reversal, along with asymmetric spirals and multiphase cluster states arising from amplitude-phase interactions. Our findings are systematically mapped onto a two-dimensional phase diagram, revealing resonance-driven bifurcation cascades. Our results illuminate how simple temporal inputs can steer complex pattern selection in nonlinear media, offering conceptual advances for systems chemistry, chemical wave control, and the design of responsive self-organizing systems.