The aim of my presentation is to present new conditions for stability for the class of system governed by linear difference equations with distributed delay, by using the Lyapunov-Krasovskii approach. This approach consists to involve stability conditions of the form of a convex optimization problem. So, I propose sufficient conditions providing the decay estimate of the response of linear difference equations with distributed delay. These conditions are less conservative than previous results in the literature. This stability analysis is extended also to the case of systems with time-varying delays. On a logistic equation with two delays: positive and negative feedback.
We would like to discuss some dynamical aspects of a logistic equation that has negative and positive delayed feedback. We present some inherent dynamics due to a combination of positive and negative delayed feedback such as unboundedness of the solution and stability of an equilibrium. For some special cases, we characterise local and global dynamics of the equation exploring in a parameter plane. This is a joint work with István Györi and Gergely Röst.