Convergence in Almost Periodic Competition Diffusion Systems

Convergence in Almost Periodic Fisher and Kolmogorov Models

We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others. The existence of an alm...

Almost Periodic Skew-symmetric Differential Systems

We study solutions of almost periodic linear differential systems. This field is called the Favard theory what is based on the famous Favard result in [10] (see, e.g., [3, Theorem 1.2] or [28, Theorem 1]). It is a well-known corollary of the Favard (and the Floquet) theory that any bounded solution of a periodic linear differential system is almost periodic (see [12, Corollary 6.5] and [13] for...

Tobias Wichtrey Control Systems with Almost Periodic

Advances in Almost Convergence

In this paper, we first give the concept of properly distributed sequence, and prove that it is almost convergent with F-limit expressed as a formal integral. Basing on these, we review the work of Feng and Li, which is shown to be a special case of our generalized theory. Then we generalize Banach limit to Banach limit functional, which is the minimum requirement to characterize strong almost ...

Almost sure exponential stability of stochastic reaction diffusion systems with Markovian jump

The stochastic reaction diffusion systems may suffer sudden shocks‎, ‎in order to explain this phenomena‎, ‎we use Markovian jumps to model stochastic reaction diffusion systems‎. ‎In this paper‎, ‎we are interested in almost sure exponential stability of stochastic reaction diffusion systems with Markovian jumps‎. ‎Under some reasonable conditions‎, ‎we show that the trivial solution of stocha...