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.

Geometrical properties of coupled oscillators at synchronization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Multistable behavior above synchronization in a locally coupled Kuramoto model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Some comments on the numerical simulation of self-synchronization of four non-ideal exciters

In this paper, self-synchronization of four non-ideal exciters is examined via numerical simulation. The mathematical model consists of four unbalanced direct Current motors with limited power supply mounted on a flexible Structural frame support. (c) 2004 Elsevier B.V. All rights reserved.

Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure

A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.

Synchronization of the unified chaotic system and application in secure communication

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On energy pumping, synchronization and beat phenomenon in a nonideal structure coupled to an essentially nonlinear oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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.

Synchronization rate, size of the ovulatory follicle, and pregnancy rate after synchronization of ovulation beginning on different days of the estrous cycle in lactating dairy cows

Recently a protocol was developed that precisely synchronizes the time of ovulation in lactating dairy cows (Ovsynch; GnRH-7d-PGF(2 alpha)-2d-GnRH). We evaluated whether initiation of Ovsynch on different days of the estrous cycle altered the effectiveness of this protocol. The percentage of cows (n=156) ovulating to the first GnRH was 64% and varied (P<0.01) by stage of estrous cycle. Treatment with PGF(2 alpha) was effective, with 93% of cows having low progesterone at second GnRH. The overall percentage of cows that ovulated after second GnRH (synchronization rate) was 87% and varied by response to first GnRH (92% if ovulation to first GnRH vs 79% if no ovulation; P<0.05). There were 6% of cows that ovulated before the second injection of GnRH and 7% with no detectable ovulation by 48 h after second GnRH. Maximal diameter of the ovulatory follicle varied by stage of estrous cycle, with cows in which Ovsynch was initiated at midcycle having the smallest follicles. In addition, milk production and serum progesterone concentration on the day of PGF(2 alpha) affected (P<0.05) size of the ovulatory follicle. Using these results we analyzed pregnancy rate at Days 28 and 98 after Al for cows (n=404) in which Ovsynch was initiated on known days of the estrous cycle. Pregnancy rate was lower for cows expected to ovulate larger follicles than those expected to ovulate smaller follicles (P<0.05; 32 vs 42%). Thus, although overall synchronization rate with Ovsynch was above, 85%, there were clear differences in response according to day of protocol initiation. Cows in which Ovsynch was initiated near midcycle had smaller ovulatory follicles and greater pregnancy rates. (C) 1999 by Elsevier B.V.