Synchronization of the unified chaotic system and application in secure communication

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On control and synchronization in chaotic and hyperchaotic systems via linear feedback control

This paper presents the control and synchronization of chaos by designing linear feedback controllers. The linear feedback control problem for nonlinear systems has been formulated under optimal control theory viewpoint. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations were provided in order to show the effectiveness of this method for the control of the chaotic Rossler system and synchronization of the hyperchaotic Rossler system. (C) 2007 Elsevier B.V. All rights reserved.

A controller design used in Lorenz synchronization chaotic system for secure communication based on LMI fuzzy control system

This paper describes a mathematical study about chaotic system and about the unified approach of chaos control via fuzzy control system based in Linear Matrix Inequality to design a controller which synchronizes the transmission/reception system. This system, that was based in Lorenz chaotic circuit, can be used for transmit signals in secure way.

Effective synchronization of a class of chua's chaotic systems using an exponential feedback coupling

A robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method. © 2013 Patrick Louodop et al.

Finite-time synchronization of tunnel-diode-based chaotic oscillators

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by PSPICE experiment are presented to show the feasibility of the proposed method.

Synchronization: Stability and duration time

We consider the problem of stability and duration of the synchronization process between self-excited oscillators, both in their regular and chaotic states. Making use of the properties of Hill equation describing the deviation between the slave and the master, we derive the stability conditions and expressions of the synchronization time. A fairly good agreement is obtained between the analytical and numerical results.

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.

Effect of timing of estradiol benzoate administration upon synchronization of ovulation in suckling Nelore cows (Bos indicus) treated with a progesterone-releasing intravaginal device

The present study investigated how the timing of the administration of estradiol benzoate (EB) impacted the synchronization of ovulation in fixed-time artificial insemination protocols of cattle. To accomplish this, two experiments were conducted, with EB injection occurring at different times: at withdrawal of the progesterone-releasing (N) intravaginal device or 24 h later. The effectiveness of these times was compared by examining ovarian follicular dynamics (Experiment 1, n = 30) and conception rates (Experiment 2, n = 504). In Experiment 1, follicular dynamics was performed in 30 Nelore cows (Bos indicus) allocated into two groups. on a random day of the estrous cycle (Day 0), both groups received 2 mg of EB i.m. and a P4-releasing intravaginal device, which was removed on Day 8, when 400 IU of eCG and 150 mu g of PGF were administered. The control group (G-EB9; n = 15) received 1 mg of EB on Day 9, while Group EB8 (G-EB8; n = 15) received the same dose a day earlier. Ovarian ultrasonographic evaluations were performed every 8 h after device removal until ovulation. The timing of EB administration (Day 8 compared with Day 9) did affect the interval between P4 device removal to ovulation (59.4 +/- 2.0 h compared with 69.3 +/- 1.7 h) and maximum diameter of dominant (1.54 +/- 0.06 a cm compared with 1.71 +/- 0.05 b cm, P = 0.03) and ovulatory (1.46 +/- 0.05 a cm compared with 1.58 +/- 0.04 b cm, P < 0.01) follicles. In Experiment 2,504 suckling cows received the same treatment described in Experiment 1, but insemination was performed as follows: Group EB8-AI48h (G-EB8-AI48h; n = 119) and Group EB8-AI54h (G-EB8-AI54h; n = 134) received 1 mg of EB on Day 8 and FrAI was performed, respectively, 48 or 54 h after P4 device removal. Group EB9-AI48h (G-EB9-AI48h; n = 126) and Group EB9-AI54h (G-EB9-AI54h n = 125) received the same treatments and underwent the same FTAI protocols as G-EB8-AI48h and G-EB8-AI54h, respectively; however, EB was administered on Day 9. Conception rates were greater (P < 0.05) in G-EB9-AI54h 163.2% (79/125) a], G-EB9-AI48h [58.7% (74/126) a] and G-EB8-AI48h [58.8% (70/119) a] than in G-EB8-AI54h [34.3% (46/134) b]. We concluded that when EB administration occurred at device withdrawal (D8), the interval to ovulation shortened and dominant and ovulatory follicle diameters decreased. Furthermore, when EB treatment was performed 24 h after device removal, FTAI conducted at either 48 or 54 h resulted in similar conception rates. However, EB treatment on the same day as device withdrawal resulted in a lesser conception rate when FTAI was conducted 54 h after device removal. (C) 2007 Elsevier B.V. All rights reserved.

Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.

Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Progesterone-based estrous synchronization protocols in non-suckled and suckled primiparous Bos indicus beef cows

In Experiment 1, effects of an intravaginal progesterone insert (CIDR) for synchronization of estrus in non-suckled cycling primiparous Bos indicus beef cows were evaluated. Cows received either no treatment (Control), prostaglandin F(2 alpha) (PGF), or CIDR (6 d)+prostaglandin F(2 alpha) (CIDR+PGF). There were greater (P<0.05) percentages of cows inseminated and pregnant in 4 d of breeding season in CIDR+PGF (81.6%; 48.7%) than in PGF (53.8%; 32.5%) and Control cows (14.6%; 8.5%). In Experiment 2, efficacy of a treatment with CIDR (6 d)+prostaglandin F(2 alpha)+48 h temporary weaning (CIDR+PGF+TW) associated or not with equine chorionic gonadotropin (eCG) for synchronization of estrus in suckled primiparous B. indicus beef cows was evaluated. Cows were assigned to receive either no treatment (Control), CIDR+PGF+TW, CIDR+PGF+TW+200 IU of eCG, or CIDR+PGF+IW+400 IU of eCG. There were greater (P<0.05) percentages of insemination and pregnancy in 4 d of breeding season in treatment groups (47.0%; 27.5%) than in Control cows(4.5%; 3.0%) and in cows treated with eCG (50.9%; 29.4%) than in cows treated only with CIDR+PGF+TW (39.4%: 23.7%). No effects of eCG dosage were detected. The percentage of cows inseminated and pregnant in a 30 d breeding season were greater (P<0.05) in cows assigned to synchronization treatments (53.3%; 37.2%) than in Control cows (35.3%; 21.4%). In the beginning of the BS, non-suckled primiparous cows treated with CIDR+PGF with estrous cycles having been initiated following calving had greater estrous detection and pregnancy rates than PGF and Control cows, and suckled primiparous cows had improved estrous detection and pregnancy rates when eCG was associated with CIDR+PGF+TW. (C) 2009 Elsevier B.V. All rights reserved.

Development of estrous synchronization protocols using melengestrol acetate in Bos indicus cattle

Five experiments were conducted on commercial farms in Brazil designed to develop the basis for an estrus synchronization protocol using melengestrol acetate (MGA) in Bos indicus cattle. These studies resulted in the development of the following protocol: 0.5 mg.d(-1) of MGA between d -14 and -1; 2.0 mg i.m. injection of estradiol cypionate on d -9; 48 h temporary weaning between d 0 and 2; and natural service beginning on d 0. The basis of this protocol was to induce estrous cyclicity before postpartum loss of body condition, prevent premature luteolysis, eliminate the need for labor required to detect estrus, and consequently increase the likelihood of pregnancy early during the postpartum period. This treatment effectively induced estrous cyclicity among anestrous cows, synchronized estrus activity, and prevented premature luteolysis with no negative effect on pregnancy.

Ovarian response of Suffolk ewes to estrous synchronization using short-term protocol

The efficacy of estrus synchronization using short-term protocol was evaluated by ultrasound exams in Suffolk ewes during the pre-breeding season. The control Group (n = 12) was synchronized by treatment for 12 days with vaginal sponges impregnated with medroxyprogesterone acetate, and 400 IU eCG at sponge withdrawal. Experimental groups I, II and III kept the sponge in place for 4 days, and 100 µg of PGF2a was administered at sponge withdrawal. Additionally, Group I (n = 12) had 0.1 mg of estradiol benzoate (EB) administered during sponge placement and 50 µg of GnRH 48 hours after sponge removal. Group II (n = 6) had 35 mg of progesterone (P4) injected, and 0.1 mg of EB administered during sponge placement, 400 IU eCG at withdrawal and 48 hours after, 50 µg GnRH were administrated. Group III (n = 12) had 35 mg of P4 and 0.2 mg of EB administered at sponge placement, 400 IU eCG at withdrawal, and 50 µg of GnRH was administrated after 56 hours. Ovaries were monitored through ultrasound scanning. Concerning the first wave, no difference was detected between the control group and the experimental groups. However, the characteristics of ovulatory wave were significantly different between the groups. The duration of the follicular wave was shorter for Group III than for Group II. The follicle in Group I reached its maximum diameter before the Group II. The diameter of the follicle at the sponge withdrawal in the control group was larger than in Group I. After sponge withdrawal, the follicular growth rate was smaller in the control group than in Group III. The maximum diameter of the follicle in Group II was larger than in the other groups. The short-term protocol in which estrogen was used did not synchronize the emergence of the wave of follicular development.