Resonant drift of three-dimensional scroll rings in periodically forced reaction-diffusion systems

Spiral waves are a well-known and intensively studied dynamic phenomenon in diverse physical, chemical, and biological systems. We investigate the impacts of periodic forcing on the dynamics of a particular threedimensional spiral wave pattern, termed the scroll ring. Numerical simulations underscore the resonance exhibited by scroll rings when the frequency of periodic forcing aligns with the rotational frequency of spiral waves. Specifically, periodically forced scroll rings demonstrate a spectrum of resonance drift behaviors, including reverse drift, accelerated or decelerated collapse, and expansion. These behaviors hinge on the initial phases of periodic forcing and spiral waves. Furthermore, we obtain a kinematic model using the perturbation theory to delineate the drift velocity of scroll rings along their radial directions as well as along their symmetry axes. This model demonstrates well congruence with numerical observations and provides predictive insights into the dynamics and control of scroll rings and wave patterns.