We consider a C 1, α smooth flow in R d which is “strongly monotone” with respect to a cone
C of rank k, a closed set that contains a linear subspace of dimension k and no linear …

We investigate the global dynamics from a measure-theoretic perspective for smooth flows
with invariant cones of rank k. For such systems, it is shown that prevalent (or equivalently …

In this paper, we study monotone properties of random and stochastic functional differential
equations and their global dynamics. First, we show that random functional differential …

The current series of papers is concerned with stochastic stability of monotone dynamical
systems by identifying the basic dynamical units that can survive in the presence of noise …

In this paper, we consider a class of almost periodically forced neutral delayed equation,
which arises from population model with delays. A threshold parameter in terms of basic …

Differentially positive systems are the nonlinear systems whose linearization along
trajectories preserves a cone field on a smooth Riemannian manifold. One of the embryonic …

For strongly monotone dynamical systems, the dynamics alternative for smooth discrete-time
systems turns out to be a perfect analogy of the celebrated Hirsch's limit-set dichotomy for …

We investigate the singularly perturbed monotone systems with respect to cones of rank $2
$ and obtain the so called Generic Poincaré-Bendixson theorem for such perturbed systems …

We focus on the presence of almost automorphy in strongly monotone skew‐product
semiflows on Banach spaces. Under the C 1 C^1‐smoothness assumption, it is shown that …

For $ C^{1} $-smooth strongly monotone discrete-time dynamical systems, it is shown that
“convergence to linearly stable cycles” is a prevalent asymptotic behavior in the measure …