We consider a model system of two coupled Hopfield neurons, which is described by delay differential equations taking into account the finite signal propagation and processing times. When the delay exceeds a critical value, a limit cycle emerges via a supercritical Hopf bifurcation. First, we calculate its frequency and trajectory perturbatively by applying the Poincaré-Lindstedt method. Then, ...

As an important feature of fingerprints, singular points (includingcores and deltas) not only represent the local ridge pattern characteristics, but also determine the topological structure (i.e. fingerprint type). In this paper, we have performed analysis for singular points in two aspects. (1) Based on the topology theory in 2D manifold, we deduced the relationship between cores and deltas in...

Carita Lindstedt*, Nathan Morehouse, Hannu Pakkanen, Jérôme Casas, Jean-Philippe Christides, Kimmo Kemppainen, Leena Lindström and Johanna Mappes Centre of Excellence in Evolutionary Research, Department of Biological and Environmental Sciences, P.O. Box 35, FI-40014 University of Jyväskylä, Jyväskylä, Finland; Department of Chemistry, P.O. Box 35, FI-40014 University of Jyväskylä, Jyväskylä, F...

A. The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene’s residue criterion. The results are compared to the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have ...

It is shown that Poincare* duality groups which satisfy the maximal condition on centralisers have a canonical decomposition as the fundamental group of a finite graph of groups in which the edge groups are polycyclic-by-finite. The results give useful information only when there are large polycyclic subgroups. Since 3-manifolds groups satisfy Max-c, the results provide a purely grouptheoretic ...

Investigators from Necker Enfants Malades Hospital, Sorbonne Paris Cite University, Raymond Poincare University, and Paris Descartes University studied motor neuron function in children with Dravet syndrome (DS).

Abstract. For the standard map the homotopically non-trivial invariant curves of rotation number ω satisfying the Bryuno condition are shown to be analytic in the perturbative parameter ε, provided |ε| is small enough. The radius of convergence ρ(ω) of the Lindstedt series – sometimes called critical function of the standard map – is studied and the relation with the Bryuno function B(ω) is der...