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.