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.