Strange attractors and their periodic repetition

In this paper, we present some important findings regarding a comprehensive characterization of dynamical behavior in the vicinity of two periodically perturbed homoclinic solutions. Using the Duffing system, we illustrate that the overall dynamical behavior of the system, including strange attractors, is organized in the form of an asymptotic invariant pattern as the magnitude of the applied periodic forcing approaches zero. Moreover, this invariant pattern repeats itself with a multiplicative period with respect to the magnitude of the forcing. This multiplicative period is an explicitly known function of the system parameters. The findings from the numerical experiments are shown to be in great agreement with the theoretical expectations.     

Strange nonchaotic attractors in Harper maps

We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.     

Strange nonchaotic attractors in random dynamical systems

Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time systems. These attractors, which are relevant to physical and biological applications, can thus be expected to occur more commonly in dynamical systems than previously thought.     

Strange Tori of the Derivative Nonlinear Schrödinger Equation

Under periodic boundary condition, the derivative nonlinear Schrödinger equation is studied. By virtue of Darboux transformations, I show that its level set can contain many disconnected tori of different dimensions. Such a picture was not seen before. I also give a formula for diffusions along these tori. The open problem on invariant manifolds is discussed.     

Strange attractors and asymptotic measures of discrete-time dissipative systems

We investigate asymptotic properties of certain discrete-time dynamical systems in two and three dimensions with solenoidal attractor. It is proved that the asymptotic measures, relevant for the generalized version of the ergodic theorem, all derive from one Haar measure.     

Strange non-chaotic attractors in a state controlled-cellular neural network-based quasiperiodically forced MLC circuit

The adsorption energies, bond order, atomic charge, optical properties, and electrostatic potential of nitrogen molecules of armchair single-walled carbon nanotubes (SWCNTs) and nitrogen-doped single-walled carbon nanotubes (N-SWCNTs) were investigated using density functional theory (DFT). Our results show that adsorption of the \(\hbox {N}_{2}\) molecules on the external wall of a nanotube is more effective than on the internal wall in SWCNTs. The results show that \(\hbox {N}_{2}\) molecule(s) are weakly bonded to SWCNTs and N-SWCNTs through van der Waals-type interactions. The interaction of \(\hbox {N}_{2}\) molecules with SWCNTs and N-SWCNTs is physisorption as the adsorption energy and charge transfer are small, and adsorption distance is large. The electronic transitions from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) (\(\hbox {H}\rightarrow \hbox {L}\)) have the maximum wavelength and the lowest oscillator strength. The potential sensor on the surface of pristine SWCNTs and N-SWCNTs for the adsorption of \(\hbox {N}_{2}\) molecule(s) is investigated. The N-loaded single-walled carbon nanotube is introduced as a better \(\hbox {N}_{2}\) molecule(s) detector when compared with SWCNTs.     

Strange particle production by antineutrinos

Cross sections are presented for antineutrino production of Λ, Σ⁰ and K⁰ in strangeness changing reactions. Associated production reactions (ΔS = 0) have been observed in the charged and the neutral current channels. For the elastic reaction $\text{v}\text{p}\text{→ μ}{}^{\mathrm{+}}\text{Λ}$, estimates have been made of the axial transition form factor.     

Generating multi-scroll chaotic attractors by thresholding

This Letter proposes a novel thresholding approach for creating multi-scroll chaotic attractors. The general jerk circuit and Chua's circuit with sine nonlinearity are then used as two representative examples to show the working principle of this method. The controlled jerk circuit can generate various limit cycles and multi-scroll chaotic attractors by tuning the thresholds and the width of inner threshold plateau. The dynamic mechanism of threshold control is further explored by analyzing the system dynamical behaviors. In particular, this approach is effective and easy to be implemented since we only need to monitor the threshold variables or their functions and then reset them if they exceed the desired thresholds. Furthermore, two simple block circuit diagrams with threshold controllers are designed for the implementations of 1, 2, 3-scroll chaotic attractors. It indicates the potential engineering applications for various chaos-based information systems.     

Statistics of strange attractors by generalized cell mapping

It is proposed in this paper to use the generalized cell mapping to locate strange attractors of dynamical systems and to determine their statistical properties. The cell-to-cell mapping method is based upon the idea of replacing the state space continuum by a large collection of state space cells and of expressing the evolution of the dynamical system in terms of a cell-to-cell mapping. This leads to a Markov chain which in turn allows us to compute all the statistical properties as well as the invariant distribution. After a general discussion, the method is applied in this paper to strange attractors of a variety of systems governed either by point mappings or by differential equations. The results indicate that it is a viable, effective and attractive method. Some comments on this method in comparison with the method of direct iteration will also be made.     

Chaotic itinerancy generated by coupling of Milnor attractors

We report the existence of chaotic itinerancy in a coupled Milnor attractor system. The attractor ruins consist of tori or local chaos generated from the original Milnor attractors. The chaotic behavior exhibited by a single orbit can be considered a "nonstationary" state, due to the extremely slow convergence of the Lyapunov exponents, but the behavior averaged over randomly chosen initial conditions is consistent with the limit theorem. We present as a possibly new indication of chaotic itinerancy the presence of slow decay of large fluctuations of the largest Lyapunov exponent.     

Chaotic behaviors and toroidal/spherical attractors generated by discontinuous dynamics

This paper reports a class of chaotic attractors with toroidal or spherical patterns. These attractors look like spheres or tori, but they are not exactly on the two-dimensional toroidal/spherical surfaces. Discontinuous structures are taken in the considered system to produce easily various chaotic tori/spheres with different input functions. Moreover, controlling the shape of these chaotic attractors can be realized by adjusting some parameters with the help of Fourier series. The underlying chaos-generation mechanism is also explored briefly.     

On the significance of reflection coefficients produced by active surfaces bounding one-dimensional sound fields

Active boundary surfaces intended to control reverberation or other characteristics of enclosed sound fields have often been investigated using plane wave tubes. This paper presents an analysis of actively terminated semi-infinite and finite-length plane wave tubes to provide needed clarification of the effects of these surfaces. By considering relationships between complex pressure-amplitude reflection coefficients and acoustic energy quantities, the investigation reveals that increases in reflection coefficient moduli at terminations do not always produce corresponding increases in total energy or energy flux in adjacent fields. These relationships are shown to depend upon physical properties of the acoustic spaces, sources, and source positions. The investigation also demonstrates how the impact of reflection coefficients with moduli exceeding unity may be easily misinterpreted.     

Computing the pressure for Axiom-A attractors by time series and large deviations for the Lyapunov exponent

For the Axiom-A attractors a relation is given between the topological pressure and the spectrum of the generalized Lyapunov exponents. As a consequence, a simple formula is found to compute the topological entropy of the attractor by means of a time series. The results are used to compute the large deviations for positive Lyapunov exponents.     

利用气体火焰研究驻波

驻波是一个比较抽象的概念,较难理解,用气体火焰模拟驻波可以让我们更直观的研究声场产生的驻波。实验中发现火焰按波形变化的规律分布,用驻波波函数和伯努利方程对实验现象进行了理论分析,引入压节(波腹)、压腹(波节)解释在两端出现的高火焰现象。实验结果与理论分析接近一致。     

Percolation transitions are not always sharpened by making networks interdependent

We study a model for coupled networks introduced recently by Buldyrev et al., [Nature (London) 464, 1025 (2010)], where each node has to be connected to others via two types of links to be viable. Removing a critical fraction of nodes leads to a percolation transition that has been claimed to be more abrupt than that for uncoupled networks. Indeed, it was found to be discontinuous in all cases studied. Using an efficient new algorithm we verify that the transition is discontinuous for coupled Erd?s-Rényi networks, but find it to be continuous for fully interdependent diluted lattices. In 2 and 3 dimensions, the order parameter exponent β is larger than in ordinary percolation, showing that the transition is less sharp, i.e., further from discontinuity, than for isolated networks. Possible consequences for spatially embedded networks are discussed.     

Dynamics of peptidergic secretory granule transport are regulated by neuronal stimulation

Background  

Peptidergic neurons store and secrete the contents of large dense core vesicles (LDCVs) from axon terminals and from dendrites. Secretion of peptides requires a highly regulated exocytotic mechanism, plus coordinated synthesis and transport of LDCVs to their sites of release. Although these trafficking events are critical to function, little is known regarding the dynamic behavior of LDCVs and the mechanisms by which their transport is regulated. Sensory neurons also package opiate receptors in peptide-containing LDCVs, which is thought to be important in pain sensation. Since peptide granules cannot be refilled locally after their contents are secreted, it is particularly important to understand how neurons support regulated release of peptides.     

Electrocortical effects of MDMA are potentiated by acoustic stimulation in rats

Background  

3,4-Methylenedioxymethamphetamine (MDMA; ecstasy) is known for its toxicological, psychopathological and abuse potential. Some environmental conditions, e.g. acoustic stimulation typical of the "rave scene" can influence the toxicity of this drug.