The dynamics of a ratio-dependent predator-prey model with two different non-constant harvesting functions depending on the predator population is studied. Equilibria and periodic orbits are computed and their stability properties are analyzed. Several bifurcations are detected as well as connecting orbits. Smooth numerical continuation is performed that allows computation of branches of soluti...

This paper concerns with the initial value problem for random set-valued functional differential equations with the second type Hukuhara derivative (RSFDEs). By using the techniques of successive approximations, the existence and uniqueness of solutions are established. Two kinds of boundedness of the solution are also established. In addition, the problem at least one solution under some condi...

We apply our recently developed global Hopf bifurcation theory to examine global continuation with respect to the parameter for periodic solutions of functional differential equationswith state-dependent delay.We give sufficient geometric conditions to ensure the uniform boundedness of periodic solutions, obtain an upper bound of the period of nonconstant periodic solutions in a connected compo...

Let G be a maximally almost periodic (MAP) Abelian group and let B be a boundedness on G in the sense of Vilenkin. We study the relations between B and the Bohr topology of G for some well known groups with boundedness (G,B). As an application, we prove that the Bohr topology of a topological group which is topologically isomorphic to the direct product of a locally convex space and an L∞-group...

We show that every isoperimetric set in R with density is bounded if the density is continuous and bounded above and below. This improves the previously known boundedness results, which basically needed a Lipschitz assumption; on the other hand, the present assumption is sharp, as we show with an explicit example. To obtain our result, we observe that the main tool which is often used, namely a...

Abstract: This paper formulates and studies a model of periodic delayed planar systems. The model can well describe many practical architecture of delayed neural networks, which is generation of some existing neural such as delayed cellular networks(DCN) and periodic delayed neural networks(PDNNS). The existence and global exponential stability of PDPNN’s periodic solutions are investigated, wi...

In this paper, we consider higher-order Hopfield neural networks (HHNNs) with time-varying delays. Based on the fixed point theorem, Lyapunov functional method, differential inequality techniques, and without assuming the boundedness on the activation functions, we establish sufficient conditions for the existence and local exponential stability of the almost periodic solutions. The results of ...