Convergence in almost periodic cooperative systems with a first integral

Convergence in Strongly Monotone Systems with an Increasing First Integral

In this paper we generalise a useful result due to J. Mierczyński which states that for a strictly cooperative system on the positive orthant, with increasing first integral, all bounded orbits are convergent. Moreover any equilibrium attracts its entire level set, and there can be no more than one equilibrium on any level set. Here, more general state spaces and more general orderings are cons...

Cooperative Irreducible Systems of Ordinary Differential Equations with First Integral

This note considers cooperative irreducible systems of ordinary differential equations admitting a C1 first integral with positive gradient. We prove that all forward or backward nonwandering points are equilibria. We obtain also some results on the global phase portrait of such systems. The main tool of proof is a canonically defined Finsler structure with respect to which the derivative skew-...

Tobias Wichtrey Control Systems with Almost Periodic

Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay

This paper considers the existence of positive almost-periodic solutions for almost-periodic LotkaVolterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.

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...