Abstract In this manuscript, quaternion-valued delayed cellular neural networks are studied. Applying the continuation theorem of coincidence degree theory, inequality techniques and a Lyapunov function approach, new sufficient condition that guarantees existence exponential stability anti-periodic solutions for is presented. The obtained results supplement some earlier publications deal with d...

in the present paper the linear oscillator in r3 with z =constanthas been considered. the aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. a newapproach based on a computational method has been used. at the end weapply our method on an example.

We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable periodic orbits move out of the unit circle. Then the periodic orbits become complex unsta...

In this paper, we study the asymptotic behavior of the solution of a semilinear problem and of a Stokes problem, with periodic data, when the size of the domain increases. In particular, we prove exponential convergence to the solution of the corresponding problem with periodic boundary conditions.

In this paper we investigate a class of nonautonomous linear parabolic problems with time-depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic and non-periodic situation. Moreover, we show that the associated evolution operator is hypercontractive.

Partial periodic patterns are an important class of regularities that exist in a time series. A key property of these patterns is that they can start, stop, and restart anywhere within a series. We classify partial periodic patterns into two types: (i) regular patterns − patterns exhibiting periodic behavior throughout a series with some exceptions and (ii) recurring patterns − patterns exhibit...

1 Introduction Harmonic resonance, subharmonic and superharmonic entrainment, quasiperiodic and chaotic behavior are well known to occur in nonlinear self-oscillating systems which are subject to periodic forcing. Harmonic resonance occurs if the periodic forcing signal has a frequency very similar to the one of the undisturbed system and results in an amplification of the oscillations.