Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels

Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal. Copyright (C) 2009 Marcio Eisencraft et al.

Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

Sensorless synchronization method for thin-film direct optical broadband monitoring system

Optical monitoring systems are necessary to manufacture multilayer thin-film optical filters with low tolerance on spectrum specification. Furthermore, to have better accuracy on the measurement of film thickness, direct monitoring is a must. Direct monitoring implies acquiring spectrum data from the optical component undergoing the film deposition itself, in real time. In making film depositions on surfaces of optical components, the high vacuum evaporator chamber is the most popular equipment. Inside the evaporator, at the top of the chamber, there is a metallic support with several holes where the optical components are assembled. This metallic support has rotary motion to promote film homogenization. To acquire a measurement of the spectrum of the film in deposition, it is necessary to pass a light beam through a glass witness undergoing the film deposition process, and collect a sample of the light beam using a spectrometer. As both the light beam and the light collector are stationary, a synchronization system is required to identify the moment at which the optical component passes through the light beam.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

Network of phase-locking oscillators and a possible model for neural synchronization

In order to model the synchronization of brain signals, a three-node fully-connected network is presented. The nodes are considered to be voltage control oscillator neurons (VCON) allowing to conjecture about how the whole process depends on synaptic gains, free-running frequencies and delays. The VCON, represented by phase-locked loops (PLL), are fully-connected and, as a consequence, an asymptotically stable synchronous state appears. Here, an expression for the synchronous state frequency is derived and the parameter dependence of its stability is discussed. Numerical simulations are performed providing conditions for the use of the derived formulae. Model differential equations are hard to be analytically treated, but some simplifying assumptions combined with simulations provide an alternative formulation for the long-term behavior of the fully-connected VCON network. Regarding this kind of network as models for brain frequency signal processing, with each PLL representing a neuron (VCON), conditions for their synchronization are proposed, considering the different bands of brain activity signals and relating them to synaptic gains, delays and free-running frequencies. For the delta waves, the synchronous state depends strongly on the delays. However, for alpha, beta and theta waves, the free-running individual frequencies determine the synchronous state. (C) 2011 Elsevier B.V. All rights reserved.

Optimized network structure for full-synchronization

A network of Kuramoto oscillators with different natural frequencies is optimized for enhanced synchronizability. All node inputs are normalized by the node connectivity and some important properties of the network Structure are determined in this case: (i) optimized networks present a strong anti-correlation between natural frequencies of adjacent nodes: (ii) this anti-correlation should be as high as possible since the average path length between nodes is maintained as small as in random networks: and (iii) high anti-correlation is obtained without any relation between nodes natural frequencies and the degree of connectivity. We also propose a network construction model with which it is shown that high anti-correlation and small average paths may be achieved by randomly rewiring a fraction of the links of a totally anti-correlated network, and that these networks present optimal synchronization properties. (C) 2008 Elsevier B.V. All rights reserved.

Chaotic Synchronization in Discrete-Time Systems Connected by Bandlimited Channels

Due to the broadband characteristic of chaotic signals, many of the methods that have been proposed for synchronizing chaotic systems do not usually present a satisfactory performance when applied to bandlimited communication channels. Here, the effects of bandwidth limitations imposed by the channel on the synchronous solution of a discrete-time chaotic master-slave network are investigated. The discrete-time system considered in this study is the Henon map. It is analytically shown that synchronism can be achieved in such a network by introducing a digital filter in the feedback loop responsible for generating the chaotic signal that will be sent to the slave node. Numerical simulations relating the filter parameters, such as its order and cut-off frequency, to the maximum Lyapunov exponent of the master node, which determines if the transmitted signal is chaotic or not, are also presented. These results can be useful for practical communication schemes based on chaos.

Effect of follicular wave synchronization on in vitro embryo production in heifers

Aiming to achieve the ideal time of ovum pick-up (OPU) for in vitro embryo production (IVP) in crossbred heifers, two Latin square design studies investigated the effect of ovarian follicular wave synchronization with estradiol benzoate (EB) and progestins. For each experiment, crossbred heifers stage of estrous cycle was synchronized either with a norgestomet ear implant (Experiment 1) or a progesterone intravaginal device (Experiment 2) for 7d, followed by the administration of 150 mu g D-cloprostenol. On Day 7, all follicles >3 mm in diameter were aspirated and implants/devices were replaced by new ones. Afterwards, implant/device replacement was conducted every 14 d. Each experiment had three treatment groups. In Experiment I (n = 12), heifers in Group 2X had their follicles aspirated twice a week and those in Groups 1X and 1X-EB were submitted to OPU once a week for a period of 28 d. Heifers from Group 1X-EB also received 2 mg EB i.m. immediately after each OPU session. In Experiment 2 (n = 11), animals from Group 0EB did not receive EB while heifers in Groups 2EB and 5EB received 2 and 5 mg of EB respectively, immediately after OPU. The OPU sessions were performed once weekly for 28 d. Therefore, in both experiments, four OPU sessions were performed in heifers aspirated once a week and in Experiment 1, eight OPU sessions were done in heifers aspirated twice a week. Additionally, during the 7-d period following follicular aspiration, ovarian ultrasonography examinations were conducted to measure diameter of the largest follicle and blood samples were collected for FSH quantification by RIA. In Experiment 1, all viable oocytes recovered were in vitro matured and fertilized. Results indicated that while progestin and EB altered follicular wave patterns, this treatment did not prevent establishment of follicular dominance on the ovaries of heifers during OPU at 7-d intervals. Furthermore, the proposed stage of follicular wave synchronization strategies did not improve the number and quality of the recovered oocytes, or the number of in vitro produced embryos. (C) 2009 Elsevier B.V. All rights reserved.

Evaluation of flow regimes in a semi-cylindrical spouted bed through statistical, mutual information, spectral and Hurst`s analysis

Hydrodynamic studies were conducted in a semi-cylindrical spouted bed column of diameter 150 mm, height 1000 mm, conical base included angle of 60 degrees and inlet orifice diameter 25 mm. Pressure transducers at several axial positions were used to obtain pressure fluctuation time series with 1.2 and 2.4 mm glass beads at U/U-ms from 0.3 to 1.6, and static bed depths from 150 to 600 mm. The conditions covered several flow regimes (fixed bed, incipient spouting, stable spouting, pulsating spouting, slugging, bubble spouting and fluidization). Images of the system dynamics were also acquired through the transparent walls with a digital camera. The data were analyzed via statistical, mutual information theory, spectral and Hurst`s Rescaled Range methods to assess the potential of these methods to characterize the spouting quality. The results indicate that these methods have potential for monitoring spouted bed operation.

Observation of generalized synchronization of chaos in a driven chaotic system

We report on the experimental observation of the generalized synchronization of chaos in a real physical system. We show that under a nonlinear resonant interaction, the chaotic dynamics of a single mode laser can become functionally related to that of a chaotic driving signal and furthermore as the coupling strength is further increased, the chaotic dynamics of the laser approaches that of the driving signal.

Stages of chaotic synchronization

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (C) 1998 American Institute of Physics.

Synchronization of estrus and fertility in zebu beef heifers treated with three estrus synchronization protocols

The effects on estrus and fertility of 3 estrus synchronization protocols were studied in Brahman beef heifers. In Treatment 1 (PGF protocol; n=234), heifers received 7.5 mg, im prostianol on Day 0 and were inseminated after observed estrus until Day 5. Treatment 2 (10-d NOR protocol; n=220) consisted of norgestomet (NOR; 3 mg, sc implant and 3 mg, im) and estradiol valerate (5 mg, im) treatment on Day -10, NOR implant removal and 400 IU, im PMSG on Day 0, and AI after observed estrus through to Day 5. Treatment 3 (14-d NOR+PGF protocol; n=168) constituted a NOR implant (3 mg, sc) on Day -14, NOR implant removal on Day 0, PGF on Day 16, and AI after observed estrus through to Day 21. All heifers were examined for return to estrus at the next cycle and inseminated after observed estrus. The heifers were then exposed to bulls for at least 21 d. During the period of estrus observation (5 d) after treatment, those heifers treated with the PGF protocol had a lower (P

Subgroup relations: A comparison of mutual intergroup differentiation and common ingroup identity models of prejudice reduction

Two studies examined relations between groups (humanities and math-science students) that implicitly or explicitly share a common superordinate category (university student). In Experiment 1, 178 participants performed a noninteractive decision-making task during which category salience was manipulated in a 2 (superordinate category salience) x 2 (subordinate category salience) between-groups design. Consistent with the mutual intergroup differentiation model, participants for whom both categories were salient exhibited the lowest levels of bias, whereas bias was strongest when the superordinate category alone was made salient. This pattern of results was replicated in Experiment 2 (N = 135). In addition, Experiment 2 demonstrated that members of subgroups that are nested within a superordinate category are more sensitive to how the superordinate category is represented than are members of subgroups that extend beyond the boundaries of the superordinate category.

Synchronization of estrus and ovulation and associated endocrine changes in Bos indicus cows

The effects of 4 estrus synchronization treatments on intervals to and synchrony of estrus and ovulation, on timing of the preovulatory LH surge and associated changes in plasma progesterone, LH, FSH, and 17 beta-estradiol (E(2)) were investigated in 48 Bos indicus cows. Treatment 1 consisted of 2 injections of PGF(2 alpha) 14 d apart (n = 12); Treatment 2 of a subcutaneous 3-mg norgestomet implant and an intramuscular injection of 3 mg of norgestomet and 5 mg estradiol valerate, with the implant removed 10 d later (n = 12; norgestomet-estradiol); Treatment 3 of norgestomet-estradiol, with a subcutaneous injection of PMSG given at time of implant removal (Day 10; n = 12); and Treatment 4 of norgestomet implant (as for Treatments 2 and 3) inserted for 10 d, with an intramuscular injection of PGF(2 alpha) given at the time of implant removal (n = 12). The experiment was conducted in 2 replicates (24 cows/replicate, 6 cows/group). Estrus, ovulation and timing of the preovulatory surge of LH varied less in cows treated with norgestomet-estradiol and PMSG than in cows in Treatments 1 and 4 (P < 0.008). Treatment with PMSG;educed variation in ovulation times and timing of the LH surge in cows treated with norgestomet-estradiol (P < 0.02). Concentrations of E(2) were higher in cows in Treatments 2 and 3 on the final day of treatment and at about 6 h post ovulation compared with cows in Treatments 1 and 4 (P < 0.05). Different methods for synchronizing estrus did not alter sequential endocrine and behavioral changes in relation to the timing of the LH peak, and the results were consistent with current recommendations for insemination times in Bos taurus cattle. (C) 1997 by Elsevier Science Inc.

Synchronization of mutually coupled chaotic systems

We report on the experimental observation of both basic frequency locking synchronization and chaos synchronization between two mutually coupled chaotic subsystems. We show that these two kinds of synchronization are two stages of interaction between coupled chaotic systems. in particular the chaos synchronization could be understood as a state of phase locking between coupled chaotic oscillations.