Synchronization of three homodromy coupled exciters in a non-resonant vibrating system of plane motion

In this paper, the synchronization problem of three homodromy coupled exciters in a non-resonant vibrating system of plane motion is studied. By introducing the average method of modified small parameters, we deduced dimensionless coupling equation of three exciters, which converted the problem of synchronization into that of the existence and stability of zero solutions for the average differential equations of the small parameters. Based on the dimensionless coupling torques and characteristics of the cor- responding limited functions, the synchronization criterion for three exciters was derived as the absolute value of dimensionless residual torque difference between arbitrary two motors being less than the maximum of their dimensionless coupling torques. The stability criterion of its synchronous state lies in the double-condition that the inertia coupling matrix is positive definite and all its elements are positive as well. The synchronization determinants are the coefficients of synchronization ability, also called as the general dynamical symmetry coefficients. The double-equilibrium state of the vibrating system is manifested by numeric method, and the numeric and simulation results derived thereof indicate the indispensable and crucial role the structural parameters of the vibrating system play in the stability criterion of synchronous operation. Besides, by adjusting its structural parameters, the elliptical motion of the vibrating system successfully met the requirements in engineering applications.

Double Position Servo Synchronous Drive System Based on Cross-Coupling Integrated Feedforward Control for Broacher

Synchronization errors directly deteriorate the machining accuracy of metal parts and the existed method cannot keep high synchronization precision because of external disturbances. A new double position servo synchronous driving scheme based on semi-closed-loop cross- coupling integrated feedforward control is proposed. The scheme comprises a position error cross-coupling feedfor-ward control and a load torque identification with feed- forward control. A digital integrated simulation system for the dual servo synchronous drive system is established. Using a 20 t servo broacher, performance analysis of the scheme is conducted based on this simulation system and the simulation results show that systems with traditional parallel or single control have problems when the work- table works with an unbalanced load. However, the system with proposed scheme shows good synchronous perfor- mance and positional accuracy. Broaching tests are performed and the experimental results show that the maximum dual axis synchronization error of the system is only 8μm during acceleration and deceleration processes and the error between the actual running position and the given position is almost zero. A double position servo synchronous driving scheme is presented based on crosscoupled integrated feedforward compensation control, which can improve the synchronization precision.

Linearly Coupled Synchronization of the New Chaotic Systems

This paper investigates synchronization within the new systems, which we denote as Liu system in this paper. New stability criteria for synchronization of linearly coupled Liu systems are attained using the Lyapunov method. Some sufficient conditions for synchronization are concluded through rigorous mathematical theory, which can be further applied to more chaotic systems. Moreover, numerical simulations are given to show the effectiveness of our synchronization criterions.

Phase synchronization and energy balance between neurons

A functional neuron has been developed from a simple neural circuit by incorporating a phototube and a thermistor in different branch circuits.The physical field energy is controlled by the photocurrent across the phototube and the channel current across the thermistor.The firing mode of this neuron is controlled synchronously by external temperature and illumination.There is energy diversity when two functional neurons are exposed to different illumination and temperature conditions.As a result,synapse connections can be created and activated in an adaptive way when field energy is exchanged between neurons.We propose two kinds of criteria to discuss the enhancement of synapse connections to neurons.The energy diversity between neurons determines the increase of the coupling intensity and synaptic current for neurons,and the realization of synchronization is helpful in maintaining energy balance between neurons.The first criterion is similar to the saturation gain scheme in that the coupling intensity is increased with a constant step within a certain period until it reaches energy balance or complete synchronization.The second criterion is that the coupling intensity increases exponentially before reaching energy balance.When two neurons become non-identical,phase synchronization can be controlled during the activation of synapse connections to neurons.For two identical neurons,the second criterion for taming synaptic intensity is effective for reaching complete synchronization and energy balance,even in the presence of noise.This indicates that a synapse connection may prefer to enhance its coupling intensity exponentially.These results are helpful in discovering why synapses are awaken and synaptic current becomes time-varying when any neurons are excited by external stimuli.The potential biophysical mechanism is that energy balance is broken and then synapse connections are activated to maintain an adaptive energy balance between the neurons.These results provide guidance for designing and training intelligent neural networks by taming the coupling channels with gradient energy distribution.

Stable anticipation synchronization in mutually coupled vertical-cavity surface-emitting lasers system

Two vertical-cavity surface-emitting lasers（VCSELs） are mutually coupled through a partially transparent mirror （PTM） placed in the pathway. The PTM plays the role of external mirror, which controls the feedback strength and coupling strength. We numerically simulate this system by establishing a visible SIMULINK model. The results demonstrate that the anticipation synchronization is achieved and it can tolerate some extent frequency detuning. Moreover, the system shows similar chaos-pass filtering effect on unidireetionally coupled system even both VCSELs are modulated. This system allows simultaneously bidirectional secure message transmission on public channels.

The Hot Spots Conjecture on a Class of Domains in R^n with n≥3

In this paper, we define a class of domains in R^n. Using the synchronous coupling of reflecting Brownian motion, we obtain the monotonicity property of the solution of the heat equation with the Neumann boundary conditions. We then show that the hot spots conjecture holds for this class of domains.