Applications, Open Problems, Alternatives
In Section 5.1 of this chapter, some polynomial models of dynamical systems from ecology and medicine are considered. In Section 5.2, the detailed global qualitative investigation of a generalized Lotka-Volterra systems is carried out. In Section 5.3, some open problems of qualitative theory of polynomial systems are stated. Sections 5.4 and 5.5 are devoted to alternative methods of the global qualitative analysis. In Section 5.4, following L. Gavrilov, the possibilities of application of the method of Abelian integrals for the study of limit cycle bifurcations are discussed. In Section 5.5, methods of algebraic and differential geometry developed in a work by N. P. Erugin for the solution of the so-called “inverse problem” of qualitative theory of dynamical systems are suggested for solving the problems stated in Section 5.3.
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