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

•The effects of periodic forcing on the dynamics of three-dimensional scroll rings are studied.•The periodically forced scroll rings demonstrate a variety of resonance behaviors with reverse drift, accelerated or slowed collapse and expansion, among others.•A kinematic model regarding the drift velocity of scroll rings under the periodic forcing both in their radial directions and along their symmetry axes is proposed.•Numerical simulations of the reaction-diffusion equations are performed, and the obtained results agree quantitatively with predictions of the kinematic model. 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 three-dimensional 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.