Stability and asymptotic properties of a system of functional differential equations with nonconstant delays

Stability of a Functional Differential System with a Finite Number of Delays

“…Criteria for stability and asymptotic stability of the solutions as well as conditions ensuring that all solutions of (2) tend to zero are derived. At the end we supplied several corollaries and an example which shows that in some cases the criteria obtained in this paper are more applicable than the criteria presented in [21].…”

“…A simple example shows that, in some cases, the results of this paper can be applied more suitably than those given in [21].…”

“…Now we show an example that, under certain circumstances, Corollary 8 is more useful than Corollary 1 from [21].…”

“…where A is supposed to be regular constant matrix, is a centre or a focus. This case is included in the case lim inf → ∞ (| ( )| − | ( )|) > 0 considered in [21], but in this special case, we are able to derive more useful results as we will see later in an example. The idea is based on the well-known result that the condition | | > | | in an autonomous equation = + ensures that zero is a focus, a centre, or a node while under the condition | Im | > | | zero can be just a focus or a centre.…”

“…Notice that, unlike the function introduced in [21], the previously defined functioñneed not be positive.…”