Characterizing chaotic melodies in automatic music composition

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests. (c) 2010 American Institute of Physics. [doi: 10.1063/1.3487516]

Particle competition for complex network community detection

In many real situations, randomness is considered to be uncertainty or even confusion which impedes human beings from making a correct decision. Here we study the combined role of randomness and determinism in particle dynamics for complex network community detection. In the proposed model, particles walk in the network and compete with each other in such a way that each of them tries to possess as many nodes as possible. Moreover, we introduce a rule to adjust the level of randomness of particle walking in the network, and we have found that a portion of randomness can largely improve the community detection rate. Computer simulations show that the model has good community detection performance and at the same time presents low computational complexity. (C) 2008 American Institute of Physics.

Transport properties in nontwist area-preserving maps

Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3247349]

Reduction of chaotic particle transport driven by drift waves in sheared flows

Investigations of chaotic particle transport by drift waves propagating in the edge plasma of tokamaks with poloidal zonal flow are described. For large aspect ratio tokamaks, the influence of radial electric field profiles on convective cells and transport barriers, created by the nonlinear interaction between the poloidal flow and resonant waves, is investigated. For equilibria with edge shear flow, particle transport is seen to be reduced when the electric field shear is reversed. The transport reduction is attributed to the robust invariant tori that occur in nontwist Hamiltonian systems. This mechanism is proposed as an explanation for the transport reduction in Tokamak Chauffage Alfven Bresilien [R. M. O. Galvao , Plasma Phys. Controlled Fusion 43, 1181 (2001)] for discharges with a biased electrode at the plasma edge.

Dynamical estimates of chaotic systems from Poincare recurrences

We show a function that fits well the probability density of return times between two consecutive visits of a chaotic trajectory to finite size regions in phase space. It deviates from the exponential statistics by a small power-law term, a term that represents the deterministic manifestation of the dynamics. We also show how one can quickly and easily estimate the Kolmogorov-Sinai entropy and the short-term correlation function by realizing observations of high probable returns. Our analyses are performed numerically in the Henon map and experimentally in a Chua's circuit. Finally, we discuss how our approach can be used to treat the data coming from experimental complex systems and for technological applications. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3263943]

Experimental observation of a complex periodic window

The existence of a special periodic window in the two-dimensional parameter space of an experimental Chua's circuit is reported. One of the main reasons that makes such a window special is that the observation of one implies that other similar periodic windows must exist for other parameter values. However, such a window has never been experimentally observed, since its size in parameter space decreases exponentially with the period of the periodic attractor. This property imposes clear limitations for its experimental detection.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Dissipation as a mechanism of energy gain

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.

Multifractal regime transition in a modified minority game model

The search for more realistic modeling of financial time series reveals several stylized facts of real markets. In this work we focus on the multifractal properties found in price and index signals. Although the usual minority game (MG) models do not exhibit multifractality, we study here one of its variants that does. We show that the nonsynchronous MG models in the nonergodic phase is multifractal and in this sense, together with other stylized facts, constitute a better modeling tool. Using the structure function (SF) approach we detected the stationary and the scaling range of the time series generated by the MG model and, from the linear (non-linear) behavior of the SF we identified the fractal (multifractal) regimes. Finally, using the wavelet transform modulus maxima (WTMM) technique we obtained its multifractal spectrum width for different dynamical regimes. (C) 2009 Elsevier Ltd. All rights reserved.

Low dimensional behavior in three-dimensional coupled map lattices

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows 1/f noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension. (c) 2008 Elsevier Ltd. All rights reserved.

Stretching and folding mechanism in foams

We have described the stretching and folding of foams in a vertical Hele-Shaw cell containing air and a surfactant solution, from a sequence of upside-down flips. Besides the firactal dimension of the foam, we have observed the logistic growth for the soap film length. The stretching and folding mechanism is present during the foam formation, and this mechanism is observed even after the foam has reached its respective maximum fractal dimension. Observing the motion of bubbles inside the foam, large bubbles present power spectrum associated with random walk motion in both directions, while the small bubbles are scattered like balls in a Galton board. (C) 2008 Published by Elsevier B.V.

EBSD characterization of an ECAP deformed Nb single crystal

A niobium single crystal was subjected to equal channel angular pressing (ECAP) at room temperature after orienting the crystal such that [1 -1 -1] ayen ND, [0 1 -1] ayen ED, and [-2 -1 -1] ayen TD. Electron backscatter diffraction (EBSD) was used to characterize the microstructures both on the transverse and the longitudinal sections of the deformed sample. After one pass of ECAP the single crystal exhibits a group of homogeneously distributed large misorientation sheets and a well formed cell structure in the matrix. The traces of the large misorientation sheets match very well with the most favorably oriented slip plane and one of the slip directions is macroscopically aligned with the simple shear plane. The lattice rotation during deformation was quantitatively estimated through comparison of the orientations parallel to three macroscopic axes before and after deformation. An effort has been made to link the microstructure with the initial crystal orientation. Collinear slip systems are believed to be activated during deformation. The full constraints Taylor model was used to simulate the orientation evolution during ECAP. The result matched only partially with the experimental observation.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

Hyperchaos in a Chua`s circuit with two new added branches

In this work a fourth-order Chua`s circuit, capable of generating hyperchaotic oscillations in a wide range of parameters, is presented. The circuit is obtained by adding two new branches to the original topology of the Chua`s double scroll circuit. One of the added branches is a linear inductor-resistor series connection, and the other one is a nonlinear voltage-controlled current source. A theoretical analysis of the circuit equations is presented, along with numerical and experimental results.

The four-element Chua`s circuit

A new circuit configuration, linearly conjugate to the standard Chua`s circuit, is presented. Its distinctive feature is that the equations now admit an additional parameter, which controls the dissipation in the network connected to the Chua diode. In the limiting case we obtain the simplest chaotic circuit, consisting of a piecewise-linear resistor and three lossless elements.