Inheritance principle in dynamical systems and an application in ecological models (Q656488)

The author develops a general principle of inheritance for a number of properties by the Poincaré map in order to obtain information on general nonautonomous models. It roughly states that, provided some local property is rough and semigroup (we refer to the paper for precise definitions), then the global map has the same property. For the example of competition models, key inherited properties (e.g. sign-invariant matrices) are specified. This approach is used to derive global stability of periodic models for various nonlinear ecological models.