The authors describe a new type of Floquet states in magnetic vortices, which arise spontaneously as a result of the nonlinear interaction between the vortex core and microwave magnons.[3][6] They show that when magnons are excited strongly enough, part of their energy is transferred to the core of the vortex, which begins to perform small circular oscillations and thus periodically modulates the magnetic state.[2][3] These oscillations lead to the creation of Floquet magnons and to a new system of oscillation frequencies that do not exist in the basic (equilibrium) state of the system.[2][6] Experiments and simulations confirm that these are stable, time-periodic states that are maintained by the internal dynamics of the system without the need for additional external temporal modulation of the parameters.[3][6] The authors analyze the spectra of these states and show a rearrangement of the magnon dispersion relation, including the formation of sidebands and avoided crossings.[1][6] The results show that magnetic vortices can serve as a model platform for investigating self-induced Floquet states and nonlinear dynamics of spin waves.[1][3] The study provides a set of data and parameters that quantitatively describe the conditions for the emergence of these states in specific nanostructures.[5][6]