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In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1le p<infty$) norms. A general approach to investigate global exponential stability in terms of various $L^{p}$ ($1le p<infty$) norms is given. Sufficient conditions ensuring global exponential stability are given, too. Comparisons of various stability criteria are given. More importantly, it is pointed out that sufficient conditions in terms of $L^{1}$ norm are enough and easy to implement in practice.
This paper is concerned with the dynamics of an infinite-dimensional gradient system under small almost periodic perturbations. Under the assumption that the original autonomous system has a global attractor given as the union of unstable manifolds o
M. Kruskal showed that each nearly-periodic dynamical system admits a formal $U(1)$ symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly-invariant manifolds of each order, near which rapid oscillations are supp
This paper concerns the long-term behavior of population systems, and in particular of chemical reaction systems, modeled by deterministic mass-action kinetics. We approach two important open problems in the field of Chemical Reaction Network Theory,
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate arose because mathematical analyses of ecosystem stability were either specific to a p
We investigate how the following properties are related to each other: i)-A manifold is transversally exponentially stable; ii)-The transverse linearization along any solution in the manifold is exponentially stable; iii)-There exists a field of posi