Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua`s circuit behavior

This paper presents an experimental characterization of the behavior of an analogous version of the Chua`s circuit. The electronic circuit signals are captured using a data acquisition board (DAQ) and processed using LabVIEW environment. The following aspects of the time series analysis are analyzed: time waveforms, phase portraits, frequency spectra, Poincar, sections, and bifurcation diagram. The circuit behavior is experimentally mapped with the parameter variations, where are identified equilibrium points, periodic and chaotic attractors, and bifurcations. These analysis techniques are performed in real-time and can be applied to characterize, with precision, several nonlinear systems.

Blowout bifurcation and spatial mode excitation in the bubbling transition to turbulence

The transition to turbulence (spatio-temporal chaos) in a wide class of spatially extended dynamical system is due to the loss of transversal stability of a chaotic attractor lying on a homogeneous manifold (in the Fourier phase space of the system) causing spatial mode excitation Since the latter manifests as intermittent spikes this has been called a bubbling transition We present numerical evidences that this transition occurs due to the so called blowout bifurcation whereby the attractor as a whole loses transversal stability and becomes a chaotic saddle We used a nonlinear three-wave interacting model with spatial diffusion as an example of this transition (C) 2010 Elsevier B V All rights reserved

Metastable Phase Diagram of Nanocrystalline ZrO(2)-Sc(2)O(3) Solid Solutions

We have investigated the crystal structures and phase transitions of nanocrystalline ZrO(2)-1 to -13 mol % Sc(2)O(3) by synchrotron X-ray powder diffraction and Raman spectroscopy. ZrO(2)-Sc(2)O(3) nanopowders were synthesized by using a stoichiometric nitrate-lysine get-combustion route. Calcination processes at 650 and at 850 degrees C yielded nanocrystalline materials with average crystallite sizes of (10 +/- 1) and (25 +/- 2) nm, respectively. Only metastable tetragonal forms and the cubic phase were identified, whereas the stable monoclinic and rhombohedral phases were not detected in the compositional range analyzed in this work. Differently from the results of investigations reported in the literature for ZrO(2)-Sc(2)O(3) materials with large crystallite sizes, this study demonstrates that, if the crystallite sizes are small enough (in the nanometric range), the metastable t ``-form of the tetragonal phase is retained. We have also determined the t`-t `` and t ``-cubic compositional boundaries at room temperature and analyzed these transitions at high temperature. Finally, using these results, we built up a metastable phase diagram for nanocrystalline compositionally homogeneous ZrO(2)-Sc(2)O(3) solid solutions that strongly differs from that previously determined from compositionally homogeneous ZrO(2)-Sc(2)O(3), Solid solutions with much larger crystallite sizes.

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

The magnetic phase diagram of Gd(2)Sn(2)O(7)

Measurements of the magnetic susceptibility of the frustrated pyrochlore magnet Gd(2)Sn(2)O(7) have been performed at temperatures below T = 5 K and in magnetic fields up to H = 12 T. The phase boundaries determined from these measurements are mapped out in an H-T phase diagram. In this gadolinium compound, where the crystal-field splitting is small and the exchange and dipolar energy are comparable, the Zeeman energy overcomes these competing energies, resulting in at least four magnetic phase transitions below 1 K. These data are compared against those for Gd(2)Ti(2)O(7) and will, we hope, stimulate further studies.

Ab initio calculation of the BCC Fe-Al-Mo (Iron-Aluminum-Molybdenum) phase diagram: Implications for the nature of the tau(2) phase

The metastable phase diagram of the BCC-based ordering equilibria in the Fe-Al-Mo system has been calculated via a truncated cluster expansion, through the combination of Full-Potential-Linear augmented Plane Wave (FP-LAPW) electronic structure calculations and of Cluster Variation Method (CVM) thermodynamic calculations in the irregular tetrahedron approximation. Four isothermal sections at 1750 K, 2000 K, 2250 K and 2500 K are calculated and correlated with recently published experimental data on the system. The results confirm that the critical temperature for the order-disorder equilibrium between Fe(3)Al-D0(3) and FeAl-B2 is increased by Mo additions, while the critical temperature for the FeAl-B2/A2 equilibrium is kept approximately invariant with increasing Mo contents. The stabilization of the Al-rich A2 phase in equilibrium with overstoichiometric B2-(Fe,Mo)Al is also consistent with the attribution of the A2 structure to the tau(2) phase, stable at high temperatures in overstoichiometric B2-FeAl. (C) 2009 Elsevier Ltd. All rights reserved.

Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Bifurcation analysis of a model for biological control

In this paper we study the Lyapunov stability and Hopf bifurcation in a biological system which models the biological control of parasites of orange plantations. (c) 2007 Elsevier Ltd. All rights reserved.

Stability and Hopf bifurcation in an hexagonal governor system

In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two. (C) 2007 Elsevier Ltd. All rights reserved.

ON THE SUPERCRITICALITY OF THE FIRST HOPF BIFURCATION IN A DELAY BOUNDARY PROBLEM

The goal of this paper is to analyze the character of the first Hopf bifurcation (subcritical versus supercritical) that appears in a one-dimensional reaction-diffusion equation with nonlinear boundary conditions of logistic type with delay. We showed in the previous work [Arrieta et al., 2010] that if the delay is small, the unique non-negative equilibrium solution is asymptotically stable. We also showed that, as the delay increases and crosses certain critical value, this equilibrium becomes unstable and undergoes a Hopf bifurcation. This bifurcation is the first one of a cascade occurring as the delay goes to infinity. The structure of this cascade will depend on the parameters appearing in the equation. In this paper, we show that the first bifurcation that occurs is supercritical, that is, when the parameter is bigger than the delay bifurcation value, stable periodic orbits branch off from the constant equilibrium.