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Autooscillation in Agate Crystallization

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Abstract

The complete qualitative analysis of dynamic model of agate crystallization is made in the vicinity of steady states of the system of two nonlinear differential equations of the first order. Calculation of the first three Liapounov 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 complete list of phase portraits of the model is performed and phase portrait with three limit cycles near one steady state is found for concrete parameter values.

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Authors and Affiliations

  1. United Institute of Geology, Geophysics and Mineralogy of the Siberian Branch of the Russian Academy of Sciences, Universitetsky Pr. 3, Novosibirsk, 630090, Russia

    N. A. Bryxina & V. S. Sheplev

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  1. N. A. Bryxina
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  2. V. S. Sheplev
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Bryxina, N.A., Sheplev, V.S. Autooscillation in Agate Crystallization. Mathematical Geology 31, 297–309 (1999). https://doi.org/10.1023/A:1007574204707

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