Reliability of linear coupling synchronization of hyperchaotic systems with unknown parameters

Complete synchronization could be reached between some chaotic and/or hyperchaotic systems under linear coupling. More generally, the conditional Lyapunov exponents are often calculated to confirm the stability of synchronization and reliability of linear controllers. In this paper, detailed proof and measurement of the reliability of linear controllers are given by constructing a Lyapunov function in the exponential form. It is confirmed that two hyperchaotic systems can reach complete synchronization when two linear controllers are imposed on the driven system unidirectionally and the unknown parameters in the driving systems are estimated completely. Finally, it gives the general guidance to reach complete synchronization under linear coupling for other chaotic and hyperchaotic systems with unknown parameters.

MULTIPLE SOLUTIONS OF SOME ELLIPTIC SYSTEMS WITH LINEAR COUPLINGS

In this paper,we study the existence of nontrivial solutions to the elliptic system {-△u=λv+Fu(x,u,v),x∈Ω,-△v=λu+Fv(x,u,v),x∈Ω,u=v=0,x∈∂Ω,where Ω■R^(N) is bounded with a smooth boundary.By the Morse theory and the Gromoll-Meyer pair,we obtain multiple nontrivial vector solutions to this system.

Chaotic synchronization in Bose Einstein condensate of moving optical lattices via linear coupling

A systematic study of the chaotic synchronization of Bose-Einstein condensed body is performed using linear cou- pling method based on Lyapunov stability theory, Sylvester＇s criterion, and Gerschgorin disc theorem. The chaotic synchro- nization of Bose-Einstein condensed body in moving optical lattices is realized by linear coupling. The relationship be- tween the synchronization time and coupling coefficient is obtained. Both the single-variable coupling and double-variable coupling are effective. The results of numerical calculation prove that the chaotic synchronization of double-variable cou- pling is faster than that of single-variable coupling and small coupling coefficient can achieve the chaotic synchronization. Weak noise has little influence on synchronization effect, so the linear coupling technology is suitable for the chaotic synchronization of Bose-Einstein condensate.

Stochastic Huge-Resonance Caused by Coupling for a Globally Coupled Linear System

In the paper, we investigate a globally coupled linear system with finite subunits subject to temporal periodic force and with multiplicative dichotomous noise. It is shown that, the global coupling among the subunits can hugely enhance the phenomenon of SR for the amplitude of the average mean field as the functions of the transition rate of the noise and that as the function of the frequency of the signal respectively.

The construction of conserved quantities for linearly coupled oscillators and study of symmetries about the conserved quantities

In this paper, the conserved quantities are constructed using two methods. The first method is by making an ansatz of the conserved quantity and then using the definition of Poisson bracket to obtain the coefficients in the ansatz. The main procedure for the second method is given as follows. Firstly, the coupled terms in Lagrangian are eliminated by changing the coordinate scales and rotating the coordinate axes, secondly, the conserved quantities are obtain in new coordinate directly, and at last, the conserved quantities are expressed in the original coordinates by using the inverse transform of the coordinates. The Noether symmetry and Lie symmetry of the infinitesimal transformations about the conserved quantities are also studied in this paper.

Synchronization and Control of Halo-Chaos in Beam Transport Network with Small World Topology

The synchronous conditions of two kinds of the small-world （SW） network are studied. The small world topology can affect on dynamical behaviors of the beam transport network （BTN） largely, if the BTN is constructed with the SW topology, the global linear coupling and special linear feedback can realize the synchronization control of beam halo-chaos as well as periodic state in the BTN with the SW topology, respectively. This important result can provide an effective way for the experimental study and the engineering design of the BTN in the high-current accelerator driven radioactive clean nuclear power systems, and may have potential use in prospective applications for halo-chaos secure communication.

Multi-goal Control of Chaotic Connected Complex Networks

Beam transport network(BTN)with small world(SW)(so-called BTN-SW)and Lorenz chaotic connectednetwork with scale-free(SF)are taken as two typical examples,we proposed a global linear coupling and combined withlocal error feedback methods in sub-networks to realize multi-goal control method of halo and chaos in two networksabove.The simulation results show that the methods above is effective for any chaotic connected networks and has apotential of applications in based-halo-chaos secure communication.

Bicharacteristic Curves in Modeling of the Earth Crust and Upper Mantle

The aim of this paper is the introduction of a new approach to 3D modelling of elastic piecewise homogeneous media, in particular Earth crust and upper Mantle. The method is based on the principle of tomography with Earthquake as a source of the signal and receiver stations on the surface. The wave propagation in solid media is described by a system of three strongly coupled hyperbolic equations with piece - wise constant coefitients. The characteristic set and hi-characteristic curves of this system are computed in a homogeneous half-space with free boundary and the formulae of reflection and diffraction of the hi-characteristics on the internal boundaries of the media. Applications of the characteristic set and bi-eharacteristic curves for the inverse problem in geophysics and Earth modelling are given.

SLIM – a formalism for linear coupled systems

A SLIM formalism to deal with a general, linearly coupled accelerator lattice is summarized. Its application to a wide range of accelerator calculations is emphasized.

Capacitive beam position monitors for the low-β beam of the Chinese ADS proton linac

Beam Position Monitors（BPMs） for the low-β beam of the Chinese Accelerator Driven Subcritical system（CADS） Proton linac are of the capacitive pick-up type.They provide higher output signals than that of the inductive type.This paper will describe the design and tests of the capacitive BPM system for the low-β proton linac,including the pick-ups,the test bench and the read-out electronics.The tests done with an actual proton beam show a good agreement between the measurements and the simulations in the time domain.

Distributed parametric modeling and simulation of light polarization states using magneto-optical sensing based on the Faraday effect

To solve the problems encountered in practical processes of magneto-optical sensing, the infinitesimal distributed-parameter model and finite-element accumulation of different dielectric properties of micromaterials were used to describe the evolution of light polarization states, instead of the previously commonly used method of lumped-parameter simulation, thus essentially explaining the mechanism of sensing, magneto-optical effects, and related factors, and achieving multiphysics coupling using the COMSOL finite-element analysis method. Considering the cases of the Faraday effect without and with line birefringence, the magneto-optical effect and output characteristics of an infinitesimal magneto-optical sensor were simulated and studied. The results verified the effectiveness of the infinitesimal sensor model. Because the magnetic field, stress, and temperature changes alter the dielectric properties of magneto-optical materials, the finite-element accumulation method lays a good foundation for research on theoretical analysis and performance of magneto-optical sensors affected by factors such as the magnetic field, temperature, and stress.