The analysis of a novel 3-D autonomous system and circuit implementation

This Letter presents a new three-dimensional autonomous system with four quadratic terms. The system with five equilibrium points has complex chaotic dynamics behaviors. It can generate many different single chaotic attractors and double coexisting chaotic attractors over a large range of parameters. We observe that these chaotic attractors were rarely reported in previous work. The complex dynamical behaviors of the system are further investigated by means of phase portraits, Lyapunov exponents spectrum, Lyapunov dimension, dissipativeness of system, bifurcation diagram and Poincaré map. The physical circuit experimental results of the chaotic attractors show agreement with numerical simulations. More importantly, the analysis of frequency spectrum shows that the novel system has a broad frequency bandwidth, which is very desirable for engineering applications such as secure communications.     

An Improved CE/SE Scheme and Its Application to Detonation Propagation

An improved two-dimensional space-time conservation element and solution element （CE/SE） method with second-order accuracy is proposed, examined and extended to simulate the detonation propagations using detailed chemical reaction models. The numerical results of planar and cellular detonation are compared with corresponding results by the Chapman-Jouguet theory and experiments, and prove that the method is a new reliable way for numerical simulations of detonation propagation.     

A novel study of parity and attractor in the time reversed Lorentz system

In this Letter, a new effective approach to achieve adaptive synchronization is proposed. Via using Ge-Yao-Chen (GYC) partial region stability theory and pragmatical asymptotically stability theorem, the numerical simulation results show that the states errors and parameter errors approach to zero much more exactly and efficiently than traditional method. The time reversed Lorenz system (called historical Lorenz system in this Letter) is introduced and used for example in this Letter. The simulation results are given in figures and tables for comparison between the new approach and traditional one to show the effectiveness and feasibility of our new strategy.     

Image encryption with chaotically coupled chaotic maps

We present a novel secure cryptosystem for direct encryption of color images, based on chaotically coupled chaotic maps. The proposed cipher provides good confusion and diffusion properties that ensures extremely high security because of the chaotic mixing of pixels’ colors. Information is mixed and distributed over a complete image using a complex strategy that makes known plaintext attack unfeasible. The encryption algorithm guarantees the three main goals of cryptography: strong cryptographic security, short encryption/decryption time, and robustness against noise and other external disturbances. Due to the high speed, the proposed cryptosystem is suitable for application in real-time communication systems.     

Multiresolution information measures applied to speech recognition

Considerable advances in automatic speech recognition have been made in the last decades, thanks specially to the use of hidden Markov models. In the field of speech signal analysis, different techniques have been developed. However, deterioration in the performance of the speech recognizers has been observed when they are trained with clean signal and tested with noisy signals. This is still an open problem in this field. Continuous multiresolution entropy has been shown to be robust to additive noise in applications to different physiological signals. In previous works we have included Shannon and Tsallis entropies, and their corresponding divergences, in different speech analysis and recognition systems. In this paper we present an extension of the continuous multiresolution entropy to different divergences and we propose them as new dimensions for the pre-processing stage of a speech recognition system. This approach takes into account information about changes in the dynamics of speech signal at different scales. The methods proposed here are tested with speech signals corrupted with babble and white noise. Their performance is compared with classical mel cepstral parametrization. The results suggest that these continuous multiresolution entropy related measures provide valuable information to the speech recognition system and that they could be considered to be included as an extra component in the pre-processing stage.     

Warp of the Invariant Circle and Onset of Chaos in Josephson Junction Equation

The dynamics of the dc and ac driving Josephson junction equation is studied in terms of the two-dimensional Poincaré map. The smooth invariant circle on the phase cylinder in over-damped case a ） 2 loses smoothness as a decreases and becomes a strange attractor eventually. This triggers two kinds of chaos, one occurs in the regions between two Arnold tongues and the other occurs within the tongues.     

Investigation of a Unified Chaotic System and Its Synchronization by Simulations*

We investigate a unified chaotic system and its synchronization including feedback synchronization and adaptive synchronization by numerical simulations. We propose a new dynamical quantity denoted by K, which connects adaptive synchronization and feedback synchronization, to analyze synchronization schemes. We find that K can estimate the smallest coupling strength for a unified chaotic system whether it is complete feedback or one-sided feedback. Based on the previous work, we also give a new dynamical method to compute the leading Lyapunov exponent.     

Turbulence in a gas laser

We test a recent assertion [A. Muriel, Physica A 388 (4) (2009) 311] that a gas consisting of excited molecules is turbulent, in contrast to the laminar state of a gas of ground state molecules. Since a lasing gas is made up of excited molecules, we examine if a lasing gas system is indeed turbulent. Surprisingly, from a literature search, it appears that turbulence in a lasing gas medium has never been addressed. To test for turbulence, we use a recently proposed criterion for the existence of turbulence, the presence of multivalued steady-state velocity fields [P. Getreur, A. Albano, A. Muriel, Phys. Lett. A 366 (2007) 101]. To study this subject, we improve an old model of a gas of two-level atoms in a one-dimensional model [A. Muriel, M. Dresden, Physica D 94 (1996) 103] by including the effect of a radiation field with the use of Einstein A and B coefficients. A set of coupled equations for the velocity fields in one dimension are derived. The zeroth order implementation of an iterative solution establishes that the steady-state velocity fields are multivalued, given by the Lambert function. We obtain signature characteristics of turbulence such as velocity reversals, infinite gradients, and stagnation points.     

Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters

This Letter investigates modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two hyperchaotic systems modified function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.     

Forbidden ordinal patterns in higher dimensional dynamics

Forbidden ordinal patterns are ordinal patterns (or rank blocks) that cannot appear in the orbits generated by a map taking values on a linearly ordered space, in which case we say that the map has forbidden patterns. Once a map has a forbidden pattern of a given length L₀, it has forbidden patterns of any length L≥L₀ and their number grows superexponentially with L. Using recent results on topological permutation entropy, in this paper we study the existence and some basic properties of forbidden ordinal patterns for self-maps on n-dimensional intervals. Our most applicable conclusion is that expansive interval maps with finite topological entropy have necessarily forbidden patterns, although we conjecture that this is also the case under more general conditions. The theoretical results are nicely illustrated for n=2 both using the naive counting estimator for forbidden patterns and Chao’s estimator for the number of classes in a population. The robustness of forbidden ordinal patterns against observational white noise is also illustrated.     

Global synchronization in arrays of coupled networks with one single time-varying delay coupling

Global synchronization in arrays of coupled networks with one single time-varying delay coupling is investigated in this Letter. A general linear coupled network with a time-varying coupling delay is proposed and its global synchronization is further discussed. Some sufficient criteria are derived based on Lyapunov functional and linear matrix inequality (LMI). It is shown that under one single delay coupling, the synchronized state changes, which is different from the conventional synchronized solution. Moreover, the degree of the nodes and the inner delayed coupling matrix play key roles in the synchronized state. In particular, the derivative of the time-varying delay can be any given value. Finally, numerical simulations are given to illustrate the theoretical results.     

Waves and patterns in ring lattices with delays

We investigate the existence and the stability of waves and phase locked states in rings of coupled oscillators with delayed interactions. Using center manifold reduction and the normal form method, we reduce the equation governing the dynamics of the whole network to an amplitude-phase model (i.e. a set of coupled ordinary differential equations describing the evolution of both the amplitudes and the phases of the oscillators). Then we prove the existence of traveling waves, in-phase and anti-phase locked oscillations, in both one-dimensional and two-dimensional lattices. The influence of the interaction strength and the number of oscillators is investigated, and the possible coexistence of waves and phase locked oscillations is shown.     

Symmetric bursting of focus-focus type in the controlled Lorenz system with two time scales

By employing a special feedback controlling scheme, a hyperchaotic Lorenz system with the structure of two time scales is constructed. Two kinds of bursting phenomena, symmetric fold/fold bursting and symmetric sub-Hopf/sub-Hopf bursting, can be observed in this system. Their respective dynamical behaviors are investigated by means of slow-fast analysis. In particular, symmetric fold/fold bursting is of focus-focus type, namely, both the up-state and the down-state are stable focus, which is different from the usual fold/fold bursting; Symmetric sub-Hopf/sub-Hopf bursting is also of focus-focus type, which has not been reported in previous work. Furthermore, phase plane analysis has been introduced to explore the evolution details of the fast subsystem for symmetric sub-Hopf/sub-Hopf bursting. With the variation of the parameter, symmetric sub-Hopf/sub-Hopf bursting can evolve to symmetric chaotic bursting or even hyperchaos.     

Effect of temperature on the electron field emission from aligned carbon nanofibers and multiwalled carbon nanotubes

Effect of temperature and aspect ratio on the field emission properties of vertically aligned carbon nanofiber and multiwalled carbon nanotube thin films were studied in detail. Carbon nanofibers and multiwalled carbon nanotube have been synthesized on Si substrates via direct current plasma enhanced chemical vapor deposition technique. Surface morphologies of the films have been studied by a scanning electron microscope, transmission electron microscope and an atomic force microscope. It is found that the threshold field and the emission current density are dependent on the ambient temperature as well as on the aspect ratio of the carbon nanostructure. The threshold field for carbon nanofibers was found to decrease from 5.1 to 2.6 V/μm when the temperature was raised from 300 to 650 K, whereas for MWCNTs it was found to decrease from 4.0 to 1.4 V/μm. This dependence was due to the change in work function of the nanofibers and nanotubes with temperature. The field enhancement factor, current density and the dependence of the effective work function with temperature and with aspect ratio were calculated and we have tried to explain the emission mechanism.     

Stability conditions, hyperchaos and control in a novel fractional order hyperchaotic system

The stability conditions in fractional order hyperchaotic systems are derived. These conditions are applied to a novel fractional order hyperchaotic system. The proposed system is also shown to exhibit hyperchaos for orders less than 4. Based on the Routh-Hurwitz conditions, the conditions for controlling hyperchaos via feedback control are also obtained. A specific condition for controlling only fractional order hyperchaotic systems is achieved. Numerical simulations are used to verify the theoretical analysis.     

Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection

A study of dynamic regimes in Bénard-Marangoni convection was carried out for various Prandtl and Marangoni numbers in small aspect ratio geometries (Γ = 2.2 and 2.8). Experiments in a small hexagonal vessel, for a large range of the Marangoni number (from 148 to 3636), were carried out. Fourier spectra and an auto-correlation function were used to recognize the various dynamic regimes. For given values of the Prandtl number (Pr = 440) and aspect ratio (Γ = 2.2), mono-periodic, bi-periodic and chaotic states were successively observed as the Marangoni number was increased. The correlation dimensions of strange attractors corresponding to the chaotic regimes were calculated. The dimensions were found to be larger than those obtained by other authors for Rayleigh-Bénard convection in aspect ratio geometries of the same order. The transition from temporal chaos to spatio-temporal chaos was also observed. For Γ = 2.2, when larger values of the Marangoni number were imposed (Ma = 1581 for Pr = 160 and Ma = 740 for Pr = 440), spatial modes were involved through the convective pattern dynamics.     

Exponential decay and scaling laws in noisy chaotic scattering

In this Letter we present a numerical study of the effect of noise on a chaotic scattering problem in open Hamiltonian systems. We use the second order Heun method for stochastic differential equations in order to integrate the equations of motion of a two-dimensional flow with additive white Gaussian noise. We use as a prototype model the paradigmatic Hénon-Heiles Hamiltonian with weak dissipation which is a well-known example of a system with escapes. We study the behavior of the scattering particles in the scattering region, finding an abrupt change of the decay law from algebraic to exponential due to the effects of noise. Moreover, we find a linear scaling law between the coefficient of the exponential law and the intensity of noise. These results are of a general nature in the sense that the same behavior appears when we choose as a model a two-dimensional discrete map with uniform noise (bounded in a particular interval and zero otherwise), showing the validity of the algorithm used. We believe the results of this work be useful for a better understanding of chaotic scattering in more realistic situations, where noise is presented.     

Synchronization Control of Two Different Chaotic Systems with Known and Unknown Parameters

Chaos synchronization of two different chaotic systems with known and unknown parameters is studied. Based on the Lyapunov stability theory, two different chaotic systems with known parameters realize global synchronization via the successfully designed nonlinear controller. By employing an adaptive synchronization scheme, the synchronization of two different chaotic systems with unknown parameters is achieved. Numerical simulations validate the effectiveness of the theoretical analysis.     

Critical curves and coexisting attractors in a quasiperiodically forced delayed system

We study three critical curves in a quasiperiodically driven system with time delays, where occurrence of symmetry-breaking and symmetry-recovering phenomena can be observed. Typical dynamical tongues involving strange nonchaotic attractors (SNAs) can be distinguished. A striking phenomenon that can be discovered is multistability and coexisting attractors in some tongues surrounding by critical curves. The blowout bifurcation accompanying with on-off intermittency can also be observed. We show that collision of attractors at a symmetric invariant subspace can lead to the appearance of symmetry-breaking.     

A special type of attractor and transitions in a delayed system

We discuss strange nonchaotic attractors (SNAs) in addition to chaotic and regular attractors in a quasiperiodically driven system with time delays. A route and the associated mechanism are described for a special type of attractor called strange-nonchaotic-attractor-like (SNA-like) through T² torus bifurcation. The type of attractor can be observed in large parameter domains and it is easily mistaken for a true SNA judging merely from the phase portrait, power spectrum and the largest Lyapunov exponent. SNA-like attractor is not strange and has no phase sensitivity. Conditions for Neimark-Sacker bifurcation are obtained by theoretical analysis for the unforced system. Complicated and interesting dynamical transitions are investigated among the different tongues.