Autooscillation in agate crystallization

The complete qualitative analysis of dynamic model of agate crystallization is made in the vicinity of steady stares of the system of two nonlinear di fferential equations of the first order: Calculation of the first three Lia pounov coefficients using the proposed numerical algorithm shows that these equations have oscillatory solutions. Types of behaviors of the system are described by behavior diagrams in terms of four parameters of model. The c omplete list of phase portraits of the model is performed and phase portrai t with three limit cycles near one steady state is found for concrete param eter values.