Uniform and strict persistence in monotone skew-product semiflows with applications to non-autonomous Nicholson systems

Producción CientíficaWe determine sufficient conditions for uniform and strict persistence in the case of skew-product semiflows generated by solutions of non-autonomous families of cooperative systems of ODEs or delay FDEs in terms of the principal spectrums of some associated linear skew-product semiflows which admit a continuous separation. Our conditions are also necessary in the linear case. We apply our results to a noncooperative almost periodic Nicholson system with a patch structure, whose persistence turns out to be equivalent to the persistence of the linearized system along the null solution.MINECO/FEDER MTM2015-6633

On Comparison Theorems for Splittings of Different Semimonotone Matrices

Comparison theorems between the spectral radii of different matrices are useful tools for judging the efficiency of preconditioners. In this paper, some comparison theorems for the spectral radii of matrices arising from proper splittings of different semimonotone matrices are presented