The flow of a $ k $-cooperative system maps the set of vectors with up to~ $(k-1) $ sign
variations to itself. In particular, $1 $-cooperative systems are just cooperative systems …

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 …

For C 1-smooth strongly monotone discrete-time dynamical systems, we prove dynamics
alternatives, which concludes that any compact orbit is either asymptotic to a linearly stable …

Positive systems play an important role in systems and control theory and have found many
applications in multiagent systems, neural networks, systems biology, and more. Positive …

We construct an integer-valued Lyapunov function σ (⋅) for generalized negative cyclic
feedback system; and prove that σ (⋅) on any ω-limit set which generated by Poincaré …

We derive a sufficient condition guaranteeing that a singularly perturbed linear time-varying
system is strongly monotone with respect to a matrix cone $ C $ of rank $ k $. This implies …

We use a general epidemic model, the SEIRS model with a general nonlinear incidence
rate, to show how the recently established generic Poincaré–Bendixson theory of flows …

For C 1-smooth flows strongly monotone with respect to cones of rank k, we prove the
pseudo-ordered principle, which concludes that the omegalimit set of a pseudo-ordered …

This paper studies limit measures of stationary measures of stochastic ordinary differential
equations on the Euclidean space and tries to determine which invariant measures of an …

An agent-based chemostat system is considered, where there exist a resource and a
consumer. Each individual of the consumer acts as an agent, which moves between patches …