Heritable properties of nonautonomous dynamical systems and their applications in competition models. (Q1398483)

For nonautonomous dynamical systems, the author substantiates the inheritance principle of their local properties by the Poincaré mapping. It means that, if a certain property is rough, locally universal and semigroup, then the global Poincaré mapping has the same property. Heritable properties are investigated both for discrete and continuous dynamical systems. An application is given to competition models between two participants, described by the system \(\dot x_1=x_1 f_1(x_1,x_2,t)\), \(\dot x_2=x_2 f_2(x_1,x_2,t)\) with smooth functions \(f_j\), \(j=1,2\), decreasing in \(x_i\) and \(T\)-periodic in \(t\).