Abstract. We present a convergence proof of the projective integration method for a class of deterministic multi-dimensional multi-scale systems which are amenable to center manifold theory. The error is shown to contain contributions associated with the numerical accuracy of the microsolver, the numerical accuracy of the macrosolver and the distance from the center manifold caused by the combi...

Motivated by the study of conditional stability of traveling waves, we give an elementary H2 center stable manifold construction for quasilinear parabolic PDE, sidestepping apparently delicate regularity issues by the combination of a carefully chosen implicit fixed-point scheme and straightforward time-weighted Hs energy estimates. As an application, we show conditional stability of Laxor unde...

We study the Kaldor-Kalecki model of business cycles with delay in both the gross product and the capital stock. Simple-zero and double-zero singularities are investigated when bifurcation parameters change near certain critical values. By performing center manifold reduction, the normal forms on the center manifold are derived to obtain the bifurcation diagrams of the model such as Hopf, homoc...

Spiral waves have been observed in several chemical systems, for instance, in the Belousov-Zhabotinsky reaction and in the catalysis on platinum surfaces. Seemingly key to the dynamics of spiral waves is the Euclidean symmetry group SE(N). In this article, an SE(N)-equivariant center-manifold reduction near meandering spirals and other waves is developed. The vector eld on the center manifold h...

We study the effective dynamics of a mechanical particle coupled to a wave field and subject to the slowly varying potential V (εq) with ε small. To lowest order in ε the motion of the particle is governed by an effective Hamiltonian. In the next order one obtains “dissipative” terms which describe the radiation reaction. We establish that this dissipative dynamics has a center manifold which i...

In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...

in the first part of this paper, some theorems are given for a riemannian manifold with semi-symmetric metric connection. in the second part of it, some special vector fields, for example, torse-forming vector fields, recurrent vector fields and concurrent vector fields are examined in this manifold. we obtain some properties of this manifold having the vectors mentioned above.

*Correspondence: [email protected]; [email protected]; [email protected] 1Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, P.R. China 2School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland Abstract In this paper, we investigate the existence of local center stable manifolds of Langevin differential equations wi...