Integrability analysis of the smallest 3D biochemical reaction model. (English) Zbl 1519.92079
Summary: In this paper the complex dynamics of a smallest biochemical system model in three-dimensional systems with the reaction scheme. This model is described by a system of three nonlinear ordinary differential equations with five positive real parameters, are analyzed and studied. We present a thorough analysis of their invariant algebraic surfaces and exponential factors and investigate the integrability and nonintegrabilty of this model. Particularly, we show the non-existence of polynomial, rational, Darboux and local analytic first integrals in a neighborhood of the equilibrium. Moreover, we prove that, the model is not integrable in the sense of Bogoyavlensky in the class of rational functions.
MSC:
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 34A30 | Linear ordinary differential equations and systems |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
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