Bifurcation of a torus from a stationary state in the presence of symmetry

We investigate the formation of a torus from a stationary state in an autonomous dynamical system with order-parameter dimensionn=4 and symmetry groupG=QC ₂ (Q =quaternion group). The quasi-periodic temporal states bifurcating from the origin due to a symmetry-induced hard-mode instability are characterized by two-independent frequencies.Dedicated to Professor Harry Thomas on the occasion of his 60th birthdayWork supported by the Sonderforschungsbereich 185 Frankfurt-Darmstadt     

Birth of bilayered torus and torus breakdown in a piecewise-smooth dynamical system

Border-collision bifurcations arise when the periodic trajectory of a piecewise-smooth system under variation of a parameter crosses into a region with different dynamics. Considering a three-dimensional map describing the behavior of a DC/DC power converter, the Letter discusses a new type of border-collision bifurcation that leads to the birth of a “bilayered torus”. This torus consists of the union of two saddle cycles, their unstable manifolds, and a stable focus cycle. When changing the parameters, the bilayered torus transforms through a border-collision bifurcation into a resonance torus containing the stable cycle and a saddle. The Letter also presents scenarios for torus destruction through homoclinic and heteroclinic tangencies.     

Synchronized oscillations in a system of two coupled van-der-pol-duffing oscillators

The results of analysis of the periodic solutions obtained within the framework of complete and truncated equations for a system of identical Van-der-Pol-Duffing oscillators with nonlinear coupling are compared. This work was presented at the Summer Workshop “Dynamic Days” (Nizhny Novgorod, June 30–July 2, 1998). Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 12, pp. 1531–1536, December, 1998.     

Mechanisms for subcritical penetration into a sandy bottom: experimental and modeling results

This paper presents preliminary results of a recent study whose overall objectives are to determine the mechanisms contributing significantly to subcritical acoustic penetration into ocean sediments, and to quantify the results for use in sonar performance prediction for the detection of buried objects. In situ acoustic measurements were performed on a sandy bottom whose geoacoustical and geomorphological properties were also measured. A parametric array mounted on a tower moving on a rail was used to insonify hydrophones located above and below the sediment interface. Data covering grazing angles both above and below the nominal critical angle and in the frequency range 2-15 kHz were acquired and processed. The results are compared to two models that account for scattering of sound at the rough water-sediment interface into the sediment. Although all possible mechanisms for subcritical penetration are not modeled, the levels predicted by both models are consistent with the levels observed in the experimental data. For the specific seafloor and experimental conditions examined, the analysis suggests that for frequencies below 5-7 kHz sound penetration into the sediment at subcritical insonification is dominated by the evanescent field, while scattering due to surface roughness is the dominant mechanism at higher frequencies.     

Bursting oscillations in a hydro-turbine governing system with two time scales

A fast-slow coupled model of the hydro-turbine governing system(HTGS)is established by introducing frequency disturbance in this paper.Based on the proposed model,the performances of two time scales for bursting oscillations in the HTGS are investigated and the effect of periodic excitation of frequency disturbance is analyzed by using the bifurcation diagrams,time waveforms and phase portraits.We find that stability and operational characteristics of the HTGS change with the value of system parameter k_d.Furthermore,the comparative analyses for the effect of the bursting oscillations on the system with different amplitudes of the periodic excitation a are carried out.Meanwhile,we obtain that the relative deviation of the mechanical torque mt rises with the increase of a.These methods and results of the study,combined with the performance of two time scales and the fast-slow coupled engineering model,provide some theoretical bases for investigating interesting physical phenomena of the engineering system.     

Cascaded synchronous terahertz optical parametric oscillations in a single MgO:PPLN crystal

We present a synchronously pumped optical parametric oscillator (OPO) based on a single MgO-doped periodically poled lithium niobate crystal (MgO:PPLN) delivering high-repetition-rate picosecond idler output in the mid-infrared. At high power levels, cascaded optical parametric oscillations are observed, from which the forward and backward idler waves are generated in the terahertz (THz) spectral region. We demonstrate the cascaded processes involving THz-wave generation and make explanations for the highorder cascaded optical parametric processes. The cascaded terahertz optical parametric oscillations in a synchronously pumped optical parametric oscillator are reported for the first time to the best of our knowledge.     

Mutual synchronization in a system of two bistable oscillators executing regular and chaotic oscillations

A numerical analysis of a new model describing two coupled modified Chua??s oscillators is conducted. Equations of a partial oscillator differ from classical equations in that the former contain additional delayed feedback in another writing of dimensionless time. Changeover from regular oscillations in the absence of additional feedback to additional-feedback-induced (switchable) chaotic oscillations is studied. It is shown that, when normal regular oscillations, as well as additional-feedback-induced chaotic oscillations, are synchronized, difference oscillations are left. They are absent only when the control parameters of partial oscillators are identical. The application of a harmonic signal allows one to control the oscillations of a chaotic system of coupled modified bistable oscillators.     

Friedel oscillations of a magnetic field penetrating into a normal metal and a size-quantized system

A magnetic field applied to a size-quantized system causes persistent equilibrium currents nonuniformly distributed across this system. For a quantum film and a two-dimensional strip, the distributions of the dia-and paramagnetic currents and magnetic field are determined. The possibility of observing field distribution by NMR is discussed.     

Scaling theory put into practice: first-principles modeling of transport in doped silicon nanowires

We combine the ideas of scaling theory and universal conductance fluctuations with density-functional theory to analyze the conductance properties of doped silicon nanowires. Specifically, we study the crossover from ballistic to diffusive transport in boron or phosphorus doped Si nanowires by computing the mean free path, sample-averaged conductance G, and sample-to-sample variations std(G) as a function of energy, doping density, wire length, and the radial dopant profile. Our main findings are (i) the main trends can be predicted quantitatively based on the scattering properties of single dopants, (ii) the sample-to-sample fluctuations depend on energy but not on doping density, thereby displaying a degree of universality, and (iii) in the diffusive regime the analytical predictions of the Dorokhov-Mello-Pereyra-Kumar theory are in good agreement with our ab initio calculations.     

Spike-burst and other oscillations in a system composed of two coupled, drastically different elements

The dynamics of a system composed of two nonlinearly coupled, drastically different nonlinear and eventually oscillatory elements is studied. The rich variety of attractors of the system is studied with the help of phase space analysis and Poincare maps. Received 19 March 1999 and Received in final form 1 November 1999     

水下同步扫描三角测距成像理论建模及仿真分析

针对激光同步扫描三角测距成像系统水下应用时,考虑不同介质界面的折射效应,通过理论建模,得出水下同步扫描三角测距成像系统的空间三维坐标测量关系表达式。分析了基线距离、接收透镜焦距等系统主要参数对距离测量分辨率的影响,以及成像探测器长度对测量范围的影响。仿真结果表明:增大基线距离和接收透镜焦距,有利于提高距离测量分辨率,增加成像探测器长度,有利于增大系统测量范围,为水下同步扫描三角测距成像系统的设计提供了理论依据。     

Singular Hopf bifurcations and mixed-mode oscillations in a two-cell inhibitory neural network

Recent studies of a firing rate model for neural competition as observed in binocular rivalry and central pattern generators [R. Curtu, A. Shpiro, N. Rubin, J. Rinzel, Mechanisms for frequency control in neuronal competition models, SIAM J. Appl. Dyn. Syst. 7 (2) (2008) 609-649] showed that the variation of the stimulus strength parameter can lead to rich and interesting dynamics. Several types of behavior were identified such as: fusion, equivalent to a steady state of identical activity levels for both neural units; oscillations due to either an escape or a release mechanism; and a winner-take-all state of bistability. The model consists of two neural populations interacting through reciprocal inhibition, each endowed with a slow negative-feedback process in the form of spike frequency adaptation. In this paper we report the occurrence of another complex oscillatory pattern, the mixed-mode oscillations (MMOs). They exist in the model at the transition between the relaxation oscillator dynamical regime and the winner-take-all regime. The system distinguishes itself from other neuronal models where MMOs were found by the following interesting feature: there is no autocatalysis involved (as in the examples of voltage-gated persistent inward currents and/or intrapopulation recurrent excitation) and therefore the two cells in the network are not intrinsic oscillators; the oscillations are instead a combined result of the mutual inhibition and the adaptation. We prove that the MMOs are due to a singular Hopf bifurcation point situated in close distance to the transition point to the winner-take-all case. We also show that in the vicinity of the singular Hopf other types of bifurcations exist and we construct numerically the corresponding diagrams.     

Bifurcation control and chaos in a linear impulsive system

Bifurcation control and the existence of chaos in a class of linear impulsive systems are discussed by means of both theoretical and numerical ways. Chaotic behaviour in the sense of Marotto's definition is rigorously proven. A linear impulsive controller, which does not result in any change in one period-1 solution of the original system, is proposed to control and anti-control chaos. The numerical results for chaotic attractor, route leading to chaos, chaos control, and chaos anti-control, which are illustrated with two examples, are in good agreement with the theoretical analysis.     

Bifurcations of oscillations of the membrane potential and the use of mappings for modeling electrically coupled neurons

In this paper, we present the results of a qualitative analysis of a generalized system of three differential equations that represent the neuron model. The main nontrivial bifurcation sets leading to the appearance of complex motions, i.e., bursts, are given. A two-dimensional mapping that models the flows generated by this system, which is considered to be the simplest model of a neuron, is proposed. The chaotic dynamics of diffusely coupled neurons is studied using the coupled mappings. This work was presented at the Summer Workshop “Dynamic Days” (Nizhny Novgorod, June 30–July 2, 1998). Lobachevsky State Univesity of Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 12, pp. 1572–1580, December, 1998.     

Bifurcation analysis and control of periodic solutions changing into invariant tori in Langford system

Bifurcation characteristics of the Langford system in a general form are systematically analysed, and nonlinear controls of periodic solutions changing into invariant tori in this system are achieved. Analytical relationship between control gain and bifurcation parameter is obtained. Bifurcation diagrams are drawn, showing the results of control for secondary Hopf bifurcation and sequences of bifurcations route to chaos. Numerical simulations of quasi-periodic tori validate analytic predictions.     

Insulator-to-metal transition in selenium-hyperdoped silicon: observation and origin

Hyperdoping has emerged as a promising method for designing semiconductors with unique optical and electronic properties, although such properties currently lack a clear microscopic explanation. Combining computational and experimental evidence, we probe the origin of sub-band-gap optical absorption and metallicity in Se-hyperdoped Si. We show that sub-band-gap absorption arises from direct defect-to-conduction-band transitions rather than free carrier absorption. Density functional theory predicts the Se-induced insulator-to-metal transition arises from merging of defect and conduction bands, at a concentration in excellent agreement with experiment. Quantum Monte Carlo calculations confirm the critical concentration, demonstrate that correlation is important to describing the transition accurately, and suggest that it is a classic impurity-driven Mott transition.