Inheritance Principle in Dynamical Systems and an Application in Ecological Models

To analyze arbitrary nonautonomous models, we develop a general principle of inheritance of a number of local properties by the Poincare period map: if some local property is rough and semigroup, then the global period map has the same property. In particular, for competition models, we specify key inherited properties (sign-invariant matrices etc.). This approach is used to prove the global stability of periodic modes for various nonlinear ecological models.