Search

Formation of disordered and ordered pore patterns in two dimensions have been reported in pore growth in nanoporous alumina templates. This is explained in terms of instability in the pattern formation. Here, we report our observation of instability in the pattern formation in three dimensions, that is, along the cylindrical axis of the pores. The instability is revealed in the form of dendrites in the pore pattern under certain fabrication conditions. We examine the conditions under which two- and three-dimensional instability occurs and compare our observations of the two dimensional case with existing models in the literature. [ABSTRACT FROM AUTHOR]

A novel chaotic adaptive butterfly mating optimization (CABMO) is proposed to be used in synthesizing the beam pattern. In order to improve the optimization accuracy and avoid trapping in the local optimum, the homogeneous chaotic system and adaptive movement mechanism are combined into the proposed algorithm, where the initialization and redistribution of butterflies are chaotically dispersed with an adaptive movement closely related to the ultraviolet changes. After validating the performance of CABMO through several benchmark functions with different dimensions, the improved algorithm outperforms when compared to other state-of-the-art nature-inspired metaheuristic algorithms. The proposed algorithm is then used to understand any linear array problems in terms of the sidelobe reduction. Finally, a CABMO strategy is utilized to optimize the mutual coupling model of the closely spaced VLF umbrella arrays. Results show that the optimized structure has comfortably outperformed the original structure. Full scanning of wave positions is realized from 15 to 30 kHz. The synthesis patterns are close to the theoretical optimum. The optimized results of the radiation performance and synthesized patterns demonstrate that the pattern synthesis and antenna structure optimization based on the CABMO algorithm provides a novel idea for antenna array optimization. [ABSTRACT FROM AUTHOR]

In the field of complex networks, how to identify influential nodes is a significant issue in analyzing the structure of a network. In the existing method proposed to identify influential nodes based on the local dimension, the global structure information in complex networks is not taken into consideration. In this paper, a node information dimension is proposed by synthesizing the local dimensions at different topological distance scales. A case study of the Netscience network is used to illustrate the efficiency and practicability of the proposed method. [ABSTRACT FROM AUTHOR]

Coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems. We have studied the parameter space of coupled Hénon maps and showed that attractors possessing unstable dimension variability (UDV) appear for parameters neighbouring the so called shrimp domains, representing parameters leading to stable periodic behaviour. Therefore, the UDV should be very likely to be found in the same large class of natural and man-made systems that present shrimp domains. [ABSTRACT FROM AUTHOR]

We consider systems of differential equations with quadratic nonlinearities having applications for biochemistry and population dynamics, which may have a large dimension n. Due to the complexity of these systems, reduction algorithms play a crucial role in study of their large time behavior. Our approach aims to reduce a large system to a smaller one consisting of m differential equations, where [ABSTRACT FROM AUTHOR]

In this Letter we consider a three parameter unfolding of a linear degeneracy corresponding to a triple-zero eigenvalue of an equilibrium point. Using blow-up techniques we obtain a system where an exact homoclinic connection is determined. The numerical continuation of this global connection shows that it exhibits three different kinds of codimension-two degeneracies. Finally, these same codimension-two homoclinic bifurcations are detected in the Rössler system, ensuring in this way the existence of chaotic dynamics. [ABSTRACT FROM AUTHOR]

Projective synchronization between two nonlinear systems with different dimension was investigated. The controllers were designed when the dimension of drive system greater than the one of response system. The opposite situation also was discussed. In addition, we found an approach to control the chaotic (hyperchaotic) system to exhibit the be-haviors of hyperchaotic (chaotic) system. The numerical simulations were implemented on different chaotic (hyperchaotic) systems, and the results indicate that our methods are effective. [ABSTRACT FROM AUTHOR]

This paper establishes the restricted isometry property for a Gabor system generated by n time-frequency shifts of a random window function in n dimensions. The sth order restricted isometry constant of the associated n × n Gabor synthesis matrix is small provided that s ≤ c n / log n. This bound provides a qualitative improvement over previous estimates, which achieve only quadratic scaling of the sparsity s with respect to n. The proof depends on an estimate for the expected supremum of a second-order chaos. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, we suggest a cryptographic protocol for symmetric key exchange based on a set of m commutative square singular matrices of dimension n× n. The suggested scheme provides a concurrent technique for users of symmetric-key cipher systems to securely exchange their private keys over public channels. This protocol is shown to possess a high level of security based on the algorithm's parameters. We also present a scheme for generating pseudorandom numbers from a single chaotic map for use in various applications, in particular, the suggested key exchange protocol.Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Modified function projective lag synchronization (MFPLS) of uncertain hyperchaotic dynamical systems with the same or different dimensions and structures is studied. Based on Lyapunov stability theory, a general theorem for controller designing, parameter update rule designing, and control gain strength adapt law designing is introduced by using adaptive controlmethod. Furthermore, the scheme is applied to four typical examples: MFPLS between two five-dimensional hyperchaotic systems with the same structures, MFPLS between two four-dimensional hyperchaotic systems with different structures, MFPLS between a four-dimensional hyperchaotic system and a three-dimensional chaotic system and MFPLS between a novel three-dimensional chaotic system, and a five-dimensional hyperchaotic system. And the system parameters are all uncertain. Corresponding numerical simulations are performed to verify and illustrate the analytical results. [ABSTRACT FROM AUTHOR]

We investigate changes in several features of the stability diagram of an optically injected single mode laser as the ratio of the photon lifetime to the carrier lifetime is progressively increased from very low values to very high values. In particular we consider the creation of a region of phase-locked bistability, changes in the nature of codimension-2 bifurcation points, and the presence or otherwise of chaos in the system. We show that many of the features associated with high values of the aforementioned ratio also emerge for very low pump currents regardless of the ratio of the lifetimes. [ABSTRACT FROM AUTHOR]

The present paper deals with fractional-order version of a dynamical system introduced by Chongxin et al. (2006). The chaotic behavior of the system is studied using analytic and numerical methods. The minimum effective dimension is identified for chaos to exist. The chaos in the proposed system is controlled using simple linear feedback controller. We design a controller to place the eigenvalues of the system Jacobian in a stable region. The effectiveness of the controller in eliminating the chaotic behavior from the state trajectories is also demonstrated using numerical simulations. Furthermore, we synchronize the system using nonlinear feedback. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we prove that the β-transformations are chaotic in the sense of both Li–Yorke and Devaney. The topological and metric properties of the sets of points with dense or non-dense orbits are investigated. We also prove the result that the set of points with non-dense orbits under the β-transformation is of full Hausdorff dimension for any . [Copyright &y& Elsevier]

Chaotic Ant Swarm (CAS) is an optimization algorithm based on swarm intelligence theory, which has been applied to find the global optimum solution in search space. However, it often loses its effectiveness and advantages when applied to large and complex problems, e.g. those with high dimensions. To resolve the problems of high computational complexity and low solution accuracy existing in CAS, we propose a Disturbance Chaotic Ant Swarm (DCAS) algorithm to significantly improve the performance of the original algorithm. The aim of this paper is achieved by three strategies which include modifying the method of updating ant's best position, neighbor selection method and establishing a self-adaptive disturbance strategy. The global convergence of the DCAS algorithm is proved in this paper. Extensive computational simulations and comparisons are carried out to validate the performance of the DCAS on two sets of benchmark functions with up to 1000 dimensions. The results show clearly that DCAS substantially enhances the performance of the CAS paradigm in terms of computational complexity, global optimality, solution accuracy and algorithm reliability for complex high-dimensional optimization problems. [ABSTRACT FROM AUTHOR]

In this study, we illustrate the fractal nature of the wake shed by a periodically flapping filament. Such wake structure is a combination of primary vortex shedding resulting in the von Kármán vortex street, a series of concentrated vortex dipoles formed when the trailing edges of filaments reach their maximum amplitudes and small eddies form along the shear layer connected with the concentrated vortices due to the shear layer instability. The vortex dynamics of the flapping filament are visualized and imaged experimentally using a soap-film flow tunnel with a high-speed camera and a low pressure sodium lamp as a light source. The wake fractal geometry is measured using the standard box-counting method and it is shown that the fractal dimension of the soap pattern boundaries in the wake is D = 1.38 ± 0.05, which agrees well with those measured for fully developed turbulences and other shear flow phenomena. The invariant of the fractality in the wake induced by the flapping filament thus provides another illustration of the geometrical self-similarity and nonlinear dynamics of chaotic fluid flows. [ABSTRACT FROM AUTHOR]

In the paper, generalized chaotic synchronization of a class of fractional order systems is studied. Based on the stability theory of linear fractional order systems, a generalized synchronization scheme is presented, and theoretical analysis is provided to verify its feasibility. The proposed method can realize generalized synchronization not only of fractional order systems with same dimension, but also of systems with different dimensions. Besides, the function relation of generalized synchronization can be linear or nonlinear. Numerical simulations show the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

We introduce a new numerical method for the study of scalar mixing in two-dimensional advection fields. The position of an advected material strip is computed kinematically, and the associated convection–diffusion problem is solved using the computed local stretching rate along the strip, assuming that the diffusing strip thickness is smaller than its local radius of curvature. This widely legitimate assumption reduces the numerical problem to the computation of a single variable along the strip, thus making the method extremely fast and applicable to any large Péclet number. The method is then used to document the mixing properties of a chaotic sine flow, for which we relate the global quantities (spectra, concentration probability distribution functions (PDFs), increments) to the distributed stretching of the strip convoluted by the flow, possibly overlapping with itself. The numerical results indicate that the PDF of the strip elongation is log normal, a signature of random multiplicative processes. This property leads to exact analytical predictions for the spectrum of the field and for the PDF of the scalar concentration of a solitary strip. The present simulations offer a unique way of discovering the interaction rule for building complex mixtures which are made of a random superposition of overlapping strips leading to concentration PDFs stable by self-convolution. [ABSTRACT FROM AUTHOR]

Abstract: The object of this paper is to reveal the relation between dynamics of the fractional system and its dimension defined as a sum of the orders of all involved derivatives. We take the fractional Lorenz system as example and regard one or three of its orders as bifurcation parameters. In this framework, we compute the corresponding bifurcation diagrams via an optimal Poincaré section technique developed by us and find there exist two routes to chaos when its dimension increases from some values to 3. One is the process of cascaded period-doubling bifurcations and the other is a crisis (boundary crisis) which occurs in the evolution of chaotic transient behavior. We would like to point out that our investigation is the first to find out that a fractional differential equations (FDEs) system can evolve into chaos by the crisis. Furthermore, we observe rich dynamical phenomena in these processes, such as two-stage cascaded period-doubling bifurcations, chaotic transients, and the transition from coexistence of three attractors to mono-existence of a chaotic attractor. These are new and interesting findings for FDEs systems which, to our knowledge, have not been described before. [Copyright &y& Elsevier]

Chaotic scattering in open Hamiltonian systems is a problem of fundamental interest with applications in several branches of physics. In this paper we analyze the effects of adding external perturbations such as dissipation and noise in chaotic scattering phenomena. Our main result is the exponential decay rate of the particles in the scattering region when the system is affected by dissipation and noise. In the case of dissipation the particles escape more slowly from the scattering region than in the conservative case. However, in the noisy case, the particles escape faster from the scattering region as compared to the noiseless case. Moreover, we analyze the fractal dimension of the set of singularities of the scattering function for the dissipative and the conservative cases. As a result of our analysis we have found that a scaling law exists between the exponential decay rate of the particles and the dissipative parameter, and that the fractal dimension for the noisy case is the unity. [ABSTRACT FROM AUTHOR]

Abstract: Two fractal dimensions and the Liapunov exponent (LE) have been applied to detect noisy output signals from UV spectrophotometer (UV), thermogravimetric analyzer (TGA) and differential scanning calorimeter (DSC) apparatus of 1-ethyl-3-methylimidazolium ethylsulfate ionic liquid ([emim][EtSO4]). The data collected from these three pieces of equipment were classified before calculating LE, regularization (RD) and box dimensions (BD). The RD and LE are able individually to detect and quantify noisy output signals with a mean error value less than 5% in all cases tested. Given that the LE can be calculated using a really simple method, this chaotic parameter has been selected as the most suitable to detect noise of signals from these apparatus. [Copyright &y& Elsevier]

Surrogate-data testing has recently been proposed as one way to detect the presence of nonlinearity and low-dimensional chaos in experimental time series. Such testing involves estimating correlation dimension for both the original data and surrogate data from which nonlinearity has been removed. We applied such testing to the same resting, eyes-closed, and eyes-open electroencephalogram (EEG) data set that was originally analyzed using dimension estimation applied only to the original data (Pritchard & Duke, 1992). Two kinds of surrogate-data sets had higher estimated dimension and poorer saturation. This indicates that the normal resting human EEG is nonlinear and therefore not a linear-stochastic system. Because nearly complete saturation at some loci was not differentially affected by the surrogate-data procedures, our results also indicate that the normal resting human EEG is high dimensional and does not represent low-dimensional chaos. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two approaches to the generalized synchronized synchronization and the inverse generalized synchronization of fractional discrete-time chaotic systems with non-identical dimensions. The convergence of the proposed approaches is established by means of recently developed stability theory. Numerical results are presented based on well-known maps in the literature. Two examples are considered: a 3D generalized synchronization and a 2D inverse generalized synchronization. [ABSTRACT FROM AUTHOR]

This paper proposed a method of generating two attractors in a novel grid multi-scroll chaotic system. Based on a newly generated three-dimensional system, a two-attractor grid multi-scroll attractor system can be generated by adding two triangular waves and a sign function. Some basic dynamical properties, such as equilibrium points, bifurcations, and phase diagrams, were studied. Furthermore, the system was experimentally confirmed by an electronic circuit. The circuit simulation results and numerical simulation results verified the feasibility of this method. [ABSTRACT FROM AUTHOR]

This paper introduces a new three dimensional autonomous system with five equilibrium points. It demonstrates complex chaotic behaviours within a wide range of parameters, which are described by phase portraits, Lyapunov exponents, frequency spectrum, etc. Analysis of the bifurcation and Poincare map is used to reveal mechanisms of generating these complicated phenomena. The corresponding electronic circuits are designed, exhibiting experimental chaotic attractors in accord with numerical simulations. Since frequency spectrum analysis shows a broad frequency bandwidth, this system has perspective of potential applications in such engineering fields as secure communication. [ABSTRACT FROM AUTHOR]