Controlling of chaos by weak periodic perturbations in Duffing-van der Pol oscillator

This paper investigates the possibility of controlling horseshoe and asymptotic chaos in the Duffing-van der Pol oscillator by both periodic parametric perturbation and addition of second periodic force. Using Melnikov method the effect of weak perturbations on horseshoe chaos is studied. Parametric regimes where suppression of horseshoe occurs are predicted. Analytical predictions are demonstrated through direct numerical simulations. Starting from asymptotic chaos we show the recovery of periodic motion for a range of values of amplitude and frequency of the periodic perturbations. Interestingly, suppression of chaos is found in the parametric regimes where the Melnikov function does not change sign.     

Inducing chaos by resonant perturbations: theory and experiment

We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.     

Towards a unified view of fluids

It has traditionally been believed that, unlike normal fluids whose structural properties are determined primarily by the intermolecular short-range repulsive interactions, the properties of polar and associating fluids are strongly affected by the long-range Coulombic interactions. In the course of investigations to determine the primary driving forces governing the behaviour of various (non-simple) fluids, and hence to gain a deeper understanding of the molecular mechanisms leading to the development of theoretically based simple models and theory, extensive and systematic computer simulations have been performed on typical quadrupolar (carbon dioxide), dipolar (acetone and acetonitrile), and associating (hydrogen fluoride, methanol, and water) fluids using the available realistic effective pair potentials and their variants involving forces of different ranges. In addition to the main structural characteristics (one- and two-dimensional site–site correlation functions, local g factors, and radial slices through the full pair correlation function), the dielectric constants and the thermodynamic properties (internal energy and pressure) of both the homogeneous liquid and supercritical fluid phases, and vapor–liquid equilibria have also been considered. Furthermore, in the case of water, the diffusion coefficient and viscosity have also been considered along with water at the interface. All the obtained results lead to the unambiguous conclusion that the structure, defined in terms of the complete set of site–site correlation functions, for both polar and associating pure fluids is governed by the same molecular mechanism as for normal fluids, i.e. by the short-range interactions (which, however, may be both repulsive and attractive), whereas the long-range part of the electrostatic forces, regardless of their strength, plays only a marginal role and may be treated as a perturbation only. The consequences of these findings for theory and applications are also discussed.     

Allometry and growth: A unified view

Allometry is crucial in biology; scaling relations are implied in laws of growth of living systems. The self similarity of Gompertzian growths of biological organisms plays a key role, in this regard, in biological similitude. The origin of allometric relationships and values of the scaling exponents is a source of debate, as well as the origin of the range of biological scales. But, besides biology, scaling and growth characterize many different complex systems. Encompassing these aspects in a unified view is an interesting target. In this paper we propose a coarse but significant model that is applied to astrophysical structures and biological organisms. The inclusion of such different systems suggests applications to fields where allometry is emerging, such as economics, urban planning and the social sciences.     

On a unified theory of electromagnetism and weak interaction

A unified theory of weak and electromagnetic interaction has been developed on the basis of the assumption that the charge and mass of a lepton is of dynamical origin. According to this model, the spontaneous breakdown of symmetry generates the photon as a Goldstone boson.     

Relativistic orbital perturbations in a weak gravitational field

With the general third-order equations of motion for a test particle, Synge's third-order orbital equations at great distance in the weak gravitational field generated by a massive body are derived. The body has an axis of symmetry around which is rotating steadily. The results found for the advance of perihelion using first integrals of motion for the general equations show that the effect due to the inner stress of the body can be derived for orbits with inclination with respect to the equator of the body. Then, by means of the variation of the parameters method, we obtain with the equations at great distance the corresponding perturbations on the elements of such orbits in the field considered. These perturbations result to be of second order with regard to the mass of the body (the basis of the approximation).     

Difficulties with a unified treatment of nonleptonic weak interactions

The isospin selection rule in a unified treatment ofCP-conserving andCP-violating nonleptonic weak interactions proposed byNishijima andSwank is investigated and compared to that of a modified version.     

基于参数非共振激励混沌抑制原理的微弱方波信号检测

利用自治混沌系统的参数非共振激励混沌抑制原理实现强噪声背景下微弱方波信号的检测. 将频率远大于系统特征频率的方波信号作为内置激励信号，经平均法处理后，得到受控系统与原系统之间的参数等效关系，并由此确定使系统由混沌状态突变为周期状态的检测参数临界值. 数值仿真结果表明此系统可以达到极低的信噪比工作下限. 相比于利用参数共振微扰混沌抑制原理实现微弱信号检测的有关方法，此方案可根据严格的理论分析得到更准确的检测参数估计值，有利于在相关领域推广应用. 关键词： 自治混沌系统 参数激励 方波信号 检测     

A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

Suppressing chaos in fractional-order systems by periodic perturbations on system variables

Based on extensive numerical and computer-graphical simulations, it is shown that fractional-order chaotic systems can be stabilized by slightly perturbing the system state variables periodically. In this chaos control scheme, the tunable parameters are chosen empirically. The effectiveness of this chaos control method is demonstrated by fractional-order Lorenz, Chen and Rössler systems, where the underlying initial value problems are numerically integrated by using the Grünwald-Letnikov method.     

Experimental suppression of chaos in a modulated multimode laser

Suppressing chaotic behavior by addition of a weak second periodic perturbation signal, which is nearly resonant to a subharmonic of the fundamental system frequency, is observed in a modulated microchip LiNdP(4)O(12) multimode laser by a highly sensitive self-mixing modulation technique. The stabilization of the unstable period-2 orbit embedded in a chaotic attractor is demonstrated in a wide parameter region. The chaos-suppressing experiments are well reproduced by simulations of globally coupled modulated Tang-Statz-deMars [J. Appl. Phys. 34 8289 (1963)] multimode laser equations, including a spatial hole-burning effect.     

Modulation and suppression of weak Cotton-Mouton effect by Faraday rotation

Polarization of electromagnetic waves in magnetized plasma is studied in conditions, when Cotton-Mouton effect is weak enough as compared with Faraday one. Evolution of polarization state is described by new mathematical approach, namely, by angular variables technique (AVT) which describes evolution of the angular parameters of polarization ellipse in magnetized plasma. The method of consequent approximations is applied, which uses the ratio (Ω _⊥/Ω ₃) of Cotton-Mouton and Faraday terms, as a small parameter of a problem and allows obtaining simple analytical expressions for azimuthal and ellipticity angles in frame of the first and second approximations. The phenomenon of ellipticity modulation and suppression by Faraday rotation is revealed, which consists in ellipticity decreasing for stronger Faraday rotation, what makes polarization closer to linear one. Numerical illustration of the phenomenon are presented. It is shown that account of the second-order terms of the method of consequent approximation provides an accuracy better than 1% even in conditions, when small parameter Ω _⊥/Ω ₃ achieves the value 1/4.     

Controlling chaos in a high dimensional system with periodic parametric perturbations

The effect of applying a periodic perturbation to an accessible parameter of a high-dimensional (coupled-Lorenz) chaotic system is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic system can result in limit cycles or significantly reduced dimension for relatively small perturbations.     

Experimental verification of the mechanisms for nonlinear harmonic growth and suppression by harmonic injection in a traveling wave tube

Understanding the generation and growth of nonlinear harmonic (and intermodulation) distortion in microwave amplifiers such as traveling wave tubes (TWTs), free electron lasers (FELs), and klystrons is of current research interest. Similar to FELs, the nonlinear harmonic growth rate scales with the harmonic number in TWTs. In klystrons, the wave number scaling applies to the nonlinear harmonic bunching and associated nonlinear space-charge waves. Using a custom-modified TWT that has sensors along the helix, we provide the first experimental confirmation of the scaling of nonlinear harmonic growth rate and wave number in TWTs. These scalings of a nonlinearly generated harmonic mode versus an injected linear harmonic mode imply that suppression by harmonic injection occurs at a single axial position that can be located as desired by changing the injected amplitude and phase.     

New realization of Chua's circuit and verification of chaos by harmonic balance analysis

Chua's circuit, which consists of two capacitors, one inductor, two resistors, one linear voltage-controlled voltage source (VCVS) and voltage-controlled current source (VCCS) type non-linear element has been realized by operational amplifiers. Various dynamical phenomena such as periodic orbit with periods T, 2T, and 4T, single scroll and double scroll similar to the Lorenz attractor have been observed experimentally by changing only the resistance value of the linear resistor R₆. The experimental observations have been confirmed by computer simulations and also using harmonic balance analysis.