A self-consistent nonlinear dynamo model is presented. The nonlinear behavior of the plasma at small scale is described by using a MHD shell model for fields fluctuations; this allow us to study the dynamo problem in a large parameter regime which characterizes the dynamo phenomenon in many natural systems and which is beyond the power of supercomputers at today. The model is able to reproduce dynamical situations in which the system can undergo transactions to different dynamo regimes. In one of these the large-scale magnetic field jumps between two states reproducing the magnetic polarity reversals. From the analysis of long time series of reversals we infer results about the statistics of persistence times, revealing the presence of hidden long-time correlations in the chaotic dynamo process.

Models of spherical dynamos are considered which involve the full interaction between the magnetic field and the motion of an incompressible conducting fluid. In the basic equations magnetic field and fluid velocity are expanded in series of certain decay modes. In this way these equations are reduced to an infinite set of ordinary first-order differential equations for the coefficients of these expansions. The behaviour of dynamos can then be studied by integrating a finite set of these equations numerically. Some first results obtained in this way are presented for mean-field models in which the growth of the magnetic field due to the α–effect is limited by large-scale motions generated by Lorentz forces.