Delay and periodicity

Periodicity in a System of Differential Equations with Finite Delay

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

Stability and periodicity in dynamic delay equations

Keywords: Delay dynamic equations Fixed point theory Lyapunov Periodic solutions Stability Time scales a b s t r a c t Let T be an arbitrary time scale that is unbounded above. By means of a variation of Lyapunov's method and contraction mapping principle this paper handles asymptotic stability of the zero solution of the completely delayed dynamic equations x ∆ (t) = −a(t)x(δ(t))δ ∆ (t). Moreo...

Periodicity in Nonlinear Systems with Infinite Delay

Using Schaefer’s fixed-point theorem, enabling us to show that if there is an a priori bound on all possible T -periodic solutions of an infinite delay Volterra difference equation, then there is a T -periodic solution. We apply our results to scalar infinite delay Volterra difference equations in which, the a priori bound is established by means of nonnegative definite Lyapunov functionals. AM...

Periodicity and knots in delay models of population growth

Recently, we investigated the effect of delay on the asymptotic behavior of the model ẋ+x = f (x(·−τ)) of population growth, when the nonlinearity f is a unimodal function. Now we prove that for large delay, there are several nonconstant (positive) periodic solutions. We also use knots theory to study periodic solutions with period 3τ . Some of our results do not rely on the continuity of f and...

Periodicity and Almost-periodicity