Bifurcations of dynamical systems with sliding : derivation of normal-form mappings

This paper is concerned with the analysis of so-called sliding bifurcations in n-dimensional piecewise-smooth dynamical systems with discontinuous vector field. These novel bifurcations occur when the system trajectory interacts with regions on the discontinuity set where sliding is possible. The derivation of appropriate normal-form maps is detailed. It is shown that the leading-order term in the map depends on the particular bifurcation scenario considered. This is in turn related to the possible bifurcation scenarios exhibited by a periodic orbit undergoing one of the sliding bifurcations discussed in the paper. A third-order relay system serves as a numerical example.</p

Leaders\u2019 competence and warmth: Their relationships with employees\u2019 well-being and organizational effectiveness

The aim of this work was to investigate competence and warmth \u2014 the two basic dimensions of social judgment \u2014 as dimensions employees use to evaluate their supervisors. A mediation model was tested in which supervisor\u2019s perceived competence and warmth were associated with relevant outcomes (lower burnout, weaker turnover intentions, more frequent citizenship behaviors) through the mediation of affective organizational commitment (AOC). In Study 1, data were collected from employees of a company in the water service sector. In Study 2, participants were financial promoters. In Study 3, the sample included employees from different organizations. As hypothesized, the perception of one\u2019s supervisor as competent (Studies 1-3) and warm (Study 3) was related to employees\u2019 lower burnout, weaker turnover intentions, more frequent prosocial behaviors through the mediation of AOC. Theoretical and practical implications of findings are discussed

Inverse proximity effect at superconductor-ferromagnet interfaces: Evidence for induced triplet pairing in the superconductor

Considerable evidence for proximity-induced triplet superconductivity on the ferromagnetic side of a superconductor-ferromagnet (S-F) interface now exists; however, the corresponding effect on the superconductor side has hardly been addressed. We have performed scanning tunneling spectroscopy measurements on NbN superconducting thin films proximity coupled to the half-metallic ferromagnet La2/3Ca1/3MnO3 (LCMO) as a function of magnetic field. We have found that at zero and low applied magnetic fields the tunneling spectra on NbN typically show an anomalous gap structure with suppressed coherence peaks and, in some cases, a zero-bias conductance peak. As the field increases to the magnetic saturation of LCMO where the magnetization is homogeneous, the spectra become more BCS-like and the critical temperature of the NbN increases, implying a reduced proximity effect. Our results therefore suggest that triplet-pairing correlations are also induced in the S side of an S-F bilayer.Comment: 12 pages, 3 figure

Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps

Resonance tongues are mode-locking regions of parameter space in which stable periodic solutions occur; they commonly occur, for example, near Neimark-Sacker bifurcations. For piecewise-smooth, continuous maps these tongues typically have a distinctive lens-chain (or sausage) shape in two-parameter bifurcation diagrams. We give a symbolic description of a class of "rotational" periodic solutions that display lens-chain structures for a general $N$-dimensional map. We then unfold the codimension-two, shrinking point bifurcation, where the tongues have zero width. A number of codimension-one bifurcation curves emanate from shrinking points and we determine those that form tongue boundaries.Comment: 27 pages, 6 figure

Sliding bifurcations : a novel mechanism for the sudden onset of chaos in dry-friction oscillators

Recent investigations of nonsmooth dynamical systems have resulted in the study of a class of novel bifurcations termed as sliding bifurcations. These bifurcations are a characteristic feature of so-called Filippov systems, that is, systems of ordinary differential equations (ODEs) with discontinuous right-hand sides. In this paper we show that sliding bifurcations also play an important role in organizing the dynamics of dry friction oscillators, which are a subclass of nonsmooth systems. After introducing the possible codimension-1 sliding bifurcations of limit cycles, we show that these bifurcations organize different types of slip to stick-slip transitions in dry friction oscillators. In particular, we show both numerically and analytically that a sliding bifurcation is an important mechanism causing the sudden jump to chaos previously unexplained in the literature on friction systems. To analyze such bifurcations we make use of a new analytical method based on the study of appropriate normal form maps describing sliding bifurcations. Also, we explain the circumstances under which the theory of so-called border-collision bifurcations can be used in order to explain the onset of complex behavior in stick-slip systems.</p

Coexisting patterns of population oscillations: the degenerate Neimark Sacker bifurcation as a generic mechanism

We investigate a population dynamics model that exhibits a Neimark Sacker bifurcation with a period that is naturally close to 4. Beyond the bifurcation, the period becomes soon locked at 4 due to a strong resonance, and a second attractor of period 2 emerges, which coexists with the first attractor over a considerable parameter range. A linear stability analysis and a numerical investigation of the second attractor reveal that the bifurcations producing the second attractor occur naturally in this type of system.Comment: 8 pages, 3 figure

Synchronization and local convergence analysis of networks with dynamic diffusive coupling

In this paper, we address the problem of achieving synchronization in networks of nonlinear units coupled by dynamic diffusive terms. We present two types of couplings consisting of a static linear term, corresponding to the diffusive coupling, and a dynamic term which can be either the integral or the derivative of the sum of the mismatches between the states of neighbouring agents. The resulting dynamic coupling strategy is a distributed proportional-integral (PI) or a proportional-derivative (PD) law that is shown to be effective in improving the network synchronization performance, for example, when the dynamics at nodes are nonidentical. We assess the stability of the network by extending the classical Master Stability Function approach to the case where the links are dynamic ones of PI/PD type. We validate our approach via a set of representative examples including networks of chaotic Lorenz and networks of nonlinear mechanical systems

Finding Exogenous Variables in Data with Many More Variables than Observations

Many statistical methods have been proposed to estimate causal models in classical situations with fewer variables than observations (p<n, p: the number of variables and n: the number of observations). However, modern datasets including gene expression data need high-dimensional causal modeling in challenging situations with orders of magnitude more variables than observations (p>>n). In this paper, we propose a method to find exogenous variables in a linear non-Gaussian causal model, which requires much smaller sample sizes than conventional methods and works even when p>>n. The key idea is to identify which variables are exogenous based on non-Gaussianity instead of estimating the entire structure of the model. Exogenous variables work as triggers that activate a causal chain in the model, and their identification leads to more efficient experimental designs and better understanding of the causal mechanism. We present experiments with artificial data and real-world gene expression data to evaluate the method.Comment: A revised version of this was published in Proc. ICANN201

Identification and characterization of PlAlix, the Alix homologue from the Mediterranean sea urchin Paracentrotus lividus.

The sea urchin provides a relatively simple and tractable system for analyzing the early stages of embryo development. Here, we use the sea urchin species, Paracentrotus lividus, to investigate the role of Alix in key stages of embryogenesis, namely the egg fertilization and the first cleavage division. Alix is a multifunctional protein involved in different cellular processes including endocytic membrane trafficking, filamentous (F)-actin remodeling, and cytokinesis. Alix homologues have been identified in different metazoans; in these organisms, Alix is involved in oogenesis and in determination/differentiation events during embryo development. Herein, we describe the identification of the sea urchin homologue of Alix, PlAlix. The deduced amino acid sequence shows that Alix is highly conserved in sea urchins. Accordingly, we detect the PlAlix protein cross-reacting with monoclonal Alix antibodies in extracts from P. lividus, at different developmental stages. Focusing on the role of PlAlix during early embryogenesis we found that PlAlix is a maternal protein that is expressed at increasingly higher levels from fertilization to the 2-cell stage embryo. In sea urchin eggs, PlAlix localizes throughout the cytoplasm with a punctuated pattern and, soon after fertilization, accumulates in larger puncta in the cytosol, and in microvilli-like protrusions. Together our data show that PlAlix is structurally conserved from sea urchin to mammals and may open new lines of inquiry into the role of Alix during the early stages of embryo development