  Context. The Blazhko effect, in RR Lyrae type stars, is a century old
mystery. Dozens of theory exists, but none have been able to entirely reproduce
the observational facts associated to this modulation phenomenon. Existing
theory all rely on the usual continuous modelization of the star. Aims. We
present a new paradigm which will not only explain the Blazhko effect, but at
the same time, will give us alternative explanations to the red limit of the
instability strip, the synchronization of layers, the mode selection and the
existence of a limit cycle for radially pulsating stars. Methods. We describe
the RR Lyrae type pulsating stars as a system of coupled nonlinear oscillators.
Considering a spatial discretisation of the star, supposing a spherical
symmetry, we develop the equation of motion and energy up to the third order in
the radial and adiabatic case. Then, we include the influence of the ionization
region as a relaxation oscillator by including elements from synchronisation
theory. Results. This discrete approach allows us to exploit existing results
in the coupled nonlinear oscillator field. For instance, the study of
synchronicity leads to an explanation of the mode selection, the layers
synchronisation, the limit cycle and the red limit of the instability strip.
But, most of all, the analogy with the Fermi-Pasta-Ulam (FPU) experiment
enables us to understand the Blazhko effect. The transfer of energy between
different modes, as induced by solitons, not only gives a plausible theory for
lightcurve modulation, but also explains the asymmetry of sidelobes.
