Considered in this paper are control systems of the form _ x 1⁄4 f ðx; uÞ. For such systems a number of related necessary conditions for various forms of stability and attractivity are presented. The paper starts by showing that Brockett’s necessary condition for stabilizability via smooth feedback still persists if f is continuous and the class of allowable u increased to include continuous fe...

Color plays an important role in human visual attention. Therefore, high color contrasts are often used for warning or information purposes (e.g. traffic signs, warning signs in industrial areas). In this work the color contrasts are evaluated in a perceptually uniform color space to achieve a human-like color classification. The results of the color analysis are organized in several feature ma...

In this paper, we study the existence and global attractivity of positive periodic solutions for impulsive predator–prey systems with dispersion and time delays. By using the method of coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solution, and by means of a suitable Lyapunov functional, the...

In this paper, we consider chemostat-type plankton models in which plankton feeds on a limiting nutrient and the nutrient is supplied at a constant rate and is partially recycled after the death of plankton by bacterial decomposition. We use a distributed delay to describe nutrient recycling and a discrete delay to model the planktonic growth response to nutrient uptake. When one or both delays...

This paper is concerned with a nonlinear dynamic equation with feedback control on time scales. Based on the theory of calculus on time scales, by using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions in shifts δ± of the system; then, by using some differential inequalities and constructing a suitable Lyapunov funct...

This paper further develops a method, originally introduced by Angeli and the second author, for proving global attractivity of steady states in certain classes of dynamical systems. In this approach, one views the given system as a negative feedback loop of a monotone controlled system. An auxiliary discrete system, whose global attractivity implies that of the original system, plays a key rol...

This paper is concerned with an almost periodic Volterra integro dynamic equation on time scales. Based on the theory of calculus on time scales, by using differential inequality theory and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the global attractivity of the system are obtained. Then, by using the properties of almost periodic func...

We apply basic tools of control theory to a chemostat model that describes the growth of one species of microorganisms that consume a limiting substrate. Under the assumption that available measurements of the model have fixed delay t>0, we design a family of feedback control laws with the objective of stabilizing the limiting substrate concentration in a fixed level. Effectiveness of this cont...

The global attractivity of the positive steady state is established for a class of nonmonotone time-delayed reaction-diffusion equations subject to the Neumann boundary condition via a fluctuation method. This result is also applied to three population models.

We study the existence and exponential attractivity of periodic solutions to Cohen-Grossberg neural network with distributed delays. Our results are obtained by applying the continuation theorem of coincidence degree theory and a general Halanay inequality.