Minimal sets in monotone and concave skew-product semiflows II:

two-dimensional systems of differential equations,

with Rafael Obaya and Ana M. Sanz,
J. Differential Equations  252 (5) (2012), 3575-3607.


Recurrent nonautonomous two-dimensional systems of differential equations of

ordinary, finite-delay and reaction-diffusion types given by cooperative and

concave vector fields define monotone and concave skew-product semiflows,

whose dynamics is analyzed in this paper. A complete description of all the

minimal sets in a very interesting dynamical situation

is provided, and some criteria to determine its possible existence

and the area on which they lie are given. Suitable examples prove the optimality

of the results.