  Many physical, chemical and biological processes rely on intrinsic
oscillations to employ resonance responses to external stimuli of certain
frequency. Such resonance phenomena in biological systems are typically
explained by one of two mechanisms: either a classical linear resonance of
harmonic oscillator, or entrainment and phase locking of nonlinear limit cycle
oscillators subjected to periodic forcing. Here, we discover a nonlinear
mechanism, which does not require intrinsic oscillations. Instead, the resonant
frequency dependence arises from coupling between an excitable and a monostable
region of the medium. This composite system is endowed with emergent
bistability between a stable steady state and stable spatiotemporal
oscillations. The resonant transition from stable state to oscillatory state is
induced by waves of particular frequency travelling through the medium. This
transition to the spatiotemporal oscillatory state requires accumulation of
multiple waves, resulting in the exclusion of lower frequencies. The cutting
off of high frequencies is realized by damping of wave amplitude in the
monostable zone and then by activating amplitude sensitive dynamics in the
monostable units. We demonstrate this new resonance mechanism in a simplistic
reaction-diffusion model. Also, we reveal this collective resonance mechanism
in in-vitro experiments and detailed biophysical simulations representing a
major type of arrhythmia. We further demonstrate, both experimentally and
theoretically, that the ongoing spatiotemporal oscillations, such as ectopic
activity in cardiac tissue, can be stopped by travelling waves of high
frequency. Overall, we claim the universality of this resonance mechanism in a
broad class of nonlinear biophysical systems. Specifically, we hypothesize that
such phenomena could be found in neuronal systems as an alternative to
traditional resonant processes.
