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

An evolutionary disc model of the edge-on galaxy NGC 5907

We present a physical model that explains the two disparate observational facts: 1) the exponential vertical disc structure in the optical and NIR of the non-obscured part of the stellar disc and 2) the enhanced FIR/submm luminosity by about a factor of four near the obscured mid-plane, which requires additional dust and also stellar light to heat the dust component. We use multi-band photometry in U, B, V, R, and I- band combined with radiative transfer through a dust component to fit simultaneously the vertical surface-brightness and colour index profiles in all bands adopting a reasonable star formation history and dynamical heating function. The final disc model reproduces the surface-brightness profiles in all bands with a moderately declining star formation rate and a slowly starting heating function for young stars. The total dust mass is 57 million solar masses as required from the FIR/submm measurements. Without a recent star burst we find in the midplane an excess of 5.2-, 4.0-, and 3.0-times more stellar light in the U-, B-, and V-band, respectively. The corresponding stellar mass-to-light ratios are 0.91 in V- and 1.0 in R-band. The central face-on optical depth in V-band is 0.81 and the radial scale length of the dust is 40% larger than that of the stellar disc. Evolutionary disc models are a powerful method to understand the vertical structure of edge-on galaxies. Insights to the star formation history and the dynamical evolution of stellar discs can be gained. FIR/submm observations are necessary to restrict the parameter space for the models.Comment: 17 pages, 12 figures (24 files), A&A in pres

Dynamical Friction in a Gaseous Medium

Using time-dependent linear perturbation theory, we evaluate the dynamical friction force on a massive perturber M_p traveling at velocity V through a uniform gaseous medium of density rho_0 and sound speed c_s. This drag force acts in the direction -\hat V, and arises from the gravitational attraction between the perturber and its wake in the ambient medium. For supersonic motion (M=V/c_s>1), the enhanced-density wake is confined to the Mach cone trailing the perturber; for subsonic motion (M<1), the wake is confined to a sphere of radius c_s t centered a distance V t behind the perturber. Inside the wake, surfaces of constant density are hyperboloids or oblate spheroids for supersonic or subsonic perturbers, respectively, with the density maximal nearest the perturber. The dynamical drag force has the form F_df= - I 4\pi (G M_p)^2\rho_0/V^2. We evaluate I analytically; its limits are I\to M^3/3 for M>1. We compare our results to the Chandrasekhar formula for dynamical friction in a collisionless medium, noting that the gaseous drag is generally more efficient when M>1 but less efficient when M<1. To allow simple estimates of orbit evolution in a gaseous protogalaxy or proto-star cluster, we use our formulae to evaluate the decay times of a (supersonic) perturber on a near-circular orbit in an isothermal \rho\propto r^{-2} halo, and of a (subsonic) perturber on a near-circular orbit in a constant-density core. We also mention the relevance of our calculations to protoplanet migration in a circumstellar nebula.Comment: 17 pages, 5 postscript figures, to appear in ApJ 3/1/9

The Isomorphism Relation Between Tree-Automatic Structures

An $\omega$-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for $\omega$-tree-automatic structures. We prove first that the isomorphism relation for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for $\omega$-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n >1) is neither a $\Sigma_2^1$-set nor a $\Pi_2^1$-set

Time--delay autosynchronization of the spatio-temporal dynamics in resonant tunneling diodes

The double barrier resonant tunneling diode exhibits complex spatio-temporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time--delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way. We compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom. The numerically obtained Floquet exponents are explained by analytical results from linear stability analysis.Comment: 10 pages, 16 figure

Major QTL for carrot color are positionally associated with carotenoid biosynthetic genes and interact epistatically in a domesticated x wild carrot cross.

We performed QTL analyses for pigment content on a carotenoid biosynthesis function map based on progeny of a wild white carrot (QAL) which accumulates no pigments x domesticated orange carrot (B493), one of the richest sources of carotenoid pigments - mainly provitamin A a - and B-carotenes

Simulations of the Hyades

Context: Using the recent observational data of R\"oser et al. we present $N$-body simulations of the Hyades open cluster. Aims: We make an attempt to determine initial conditions of the Hyades cluster at the time of its formation in order to reproduce the present-day cumulative mass profile, stellar mass and luminosity function (LF). Methods: We performed direct $N$-body simulations of the Hyades in an analytic Milky Way potential that account for stellar evolution and include primordial binaries in a few models. Furthermore, we applied a Kroupa (2001) IMF and used extensive ensemble-averaging. Results: We find that evolved single-star King initial models with King parameters $W_0 = 6-9$ and initial particle numbers $N_0 = 3000$ provide good fits to the observational present-day cumulative mass profile within the Jacobi radius. The best-fit King model has an initial mass of $1721\ M_\odot$ and an average mass loss rate of $-2.2 \ M_\odot/\mathrm{Myr}$. The K-band LFs of models and observations show a reasonable agreement. Mass segregation is detected in both observations and models. If 33% primordial binaries are included the initial particle number is reduced by 5% as compared to the model without primordial binaries. Conclusions: The present-day properties of the Hyades can be well reproduced by a standard King or Plummer initial model when choosing appropriate initial conditions. The degeneracy of good-fitting models can be quite high due to the large dimension of the parameter space. More simulations with different Roche-lobe filling factors and primordial binary fractions are required to explore this degeneracy in more detail.Comment: 14 pages, 16+1 figures, hopefully final version, contains a note added in proo

Bifurcations in Globally Coupled Map Lattices

The dynamics of globally coupled map lattices can be described in terms of a nonlinear Frobenius--Perron equation in the limit of large system size. This approach allows for an analytical computation of stationary states and their stability. The complete bifurcation behaviour of coupled tent maps near the chaotic band merging point is presented. Furthermore the time independent states of coupled logistic equations are analyzed. The bifurcation diagram of the uncoupled map carries over to the map lattice. The analytical results are supplemented with numerical simulations.Comment: 19 pages, .dvi and postscrip

Relation between coupled map lattices and kinetic Ising models

A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity to a symmetry breaking bifurcation point. In parameter space four phases with different ergodic behaviour are observed. Although the coupling in the map lattice is diffusive, antiferromagnetic ordering is predominant. Via coarse graining the deterministic model is mapped to a master equation which establishes an equivalence between our system and a kinetic Ising model. Such an approach sheds some light on the dependence of the transient behaviour on the system size and the nature of the phase transitions.Comment: 15 pages, figures included, Phys. Rev. E in pres

Chemical gradients in the Milky Way from the RAVE data: II. Giant stars

Aims. We provide new constraints on the chemo-dynamical models of the Milky Way by measuring the radial and vertical chemical gradients for the elements Mg, Al, Si, Ti, and Fe in the Galactic disc and the gradient variations as a function of the distanc