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

作者：Obaya Rafael^*; Sanz Ana M

来源：Journal of Differential Equations, 2016, 261(7): 4135-4163.

DOI：10.1016/j.jde.2016.06.019

• Non-autonomous dynamical systems
• Uniform and strict persistence
• Non-autonomous Nicholson systems

We determine sufficient conditions for uniform and strict persistence in the case of skew-product semi flows 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.

• 出版日期2016-10-5