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  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.
KeywordsSingular Point Lyapunov Function Hopf Bifurcation Polynomial System Singular System
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