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

Rafael Obaya, Ana M. Sanz
2016 Journal of Differential Equations  
We determine sufficient conditions for uniform and strict persistence in the case of skew-product semiflows generated by solutions of nonautonomous 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
more » ... out to be equivalent to the persistence of the linearized system along the null solution. 2010 Mathematics Subject Classification. 37C60, 37C65, 92D25. Key words and phrases. Non-autonomous dynamical systems, uniform and strict persistence, non-autonomous Nicholson systems.
doi:10.1016/j.jde.2016.06.019 fatcat:v6b5ok2oyjhx7cduhwjnvuarku