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Qualitative investigation of a gene model using computer algebra algorithms

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Using algorithms and packages for computer algebra, we investigate a three-dimensional autonomous system of ordinary differential equations (ODEs) used in [1] to simulate the dynamics of a gene. A computational approach based on elimination theory algorithms is proposed to find invariant surfaces of multidimensional polynomial differential equation systems; this approach allows one to reduce the investigation of the system dynamics to studying the dynamics of a lower-order system. In addition, an effective approach based on the Lyapunov function is proposed to investigate the Andronov-Hopf bifurcation; this approach is used to find such bifurcations in the model under study.

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Correspondence to M. Han.

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Original Russian Text © F. Boulier, M. Han, F. Lemaire, V.G. Romanovski, 2015, published in Programmirovanie, 2015, Vol. 41, No. 2.

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Boulier, F., Han, M., Lemaire, F. et al. Qualitative investigation of a gene model using computer algebra algorithms. Program Comput Soft 41, 105–111 (2015).

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