Uniform persistence and upper Lyapunov exponents for monotone skew-product semiflows (Q2852516)

The authors study the problem of uniform persistence above and below a minimal set in the context of abstract monotone skew-product semi-flows. Two concepts describing a continuous separation of the state space are introduced, where the latter one is particularly suitable in the context of functional differential equations. Under an additional assumption on the principal spectrum (a type of dynamical spectrum), a condition for uniform peristence is given.NEWLINENEWLINEThese results are improved when dealing with concrete equations of ordinary differential, delay or parabolic type. In this process, a new method to compute the upper Lyapunov exponent of a minimal set is presented. The carefully written and interesting paper closes with conditions for uniform persistence under additional sublinearity, concavity or convexity assumptions. Moreover, an application to neural networks is given.