ABSTRACT
In this work, we consider a ring of coupled electronic (Wien-bridge) oscillators from a perspective combining modeling, simulation, and experimental observation. Following up on earlier work characterizing the pairwise interaction of Wien-bridge oscillators by Kuramoto-Sakaguchi phase dynamics, we develop a lattice model for a chain thereof, featuring an exponentially decaying spatial kernel. We find that for certain values of the Sakaguchi parameter α, states of traveling phase-domain fronts involving the coexistence of two clearly separated regions of distinct dynamical behavior, can establish themselves in the ring lattice. Experiments and simulations show that stationary coexistence domains of synchronization only manifest themselves with the introduction of a local impurity; here an incoherent cluster of oscillators can arise reminiscent of the chimera states in a range of systems with homogeneous oscillators and suitable nonlocal interactions between them.
ABSTRACT
We derive the Kuramoto-Sakaguchi model from the basic circuit equations governing two coupled Wien-bridge oscillators. A Wien-bridge oscillator is a particular realization of a tunable autonomous oscillator that makes use of frequency filtering (via an RC bandpass filter) and positive feedback (via an operational amplifier). In the past few years, such oscillators have started to be utilized in synchronization studies. We first show that the Wien-bridge circuit equations can be cast in the form of a coupled pair of van der Pol equations. Subsequently, by applying the method of multiple time scales, we derive the differential equations that govern the slow evolution of the oscillator phases and amplitudes. These equations are directly reminiscent of the Kuramoto-Sakaguchi-type models for the study of synchronization. We analyze the resulting system in terms of the existence and stability of various coupled oscillator solutions and explain on that basis how their synchronization emerges. The phase-amplitude equations are also compared numerically to the original circuit equations and good agreement is found. Finally, we report on experimental measurements of two coupled Wien-bridge oscillators and relate the results to the theoretical predictions.
ABSTRACT
PURPOSE: The aim of our study was to investigate the impact of anti-thyroid peroxidase antibodies (Anti-TPO) on pregnancy outcome following the in vitro fertilization and embryo transfer (IVF-ET) in general groups and in subgroups divided according to AMH level and age. METHODS: A total of 114 patients positive for anti-thyroid peroxidase antibodies (Anti-TPO+ group) and 495 infertile women negative for anti-thyroid peroxidase antibodies (Anti-TPO- group) undergoing IVF with ICSI from April 2010 to April 2012 were analyzed retrospectively. RESULTS: There were no significant differences in age, BMI, basal FSH, LH, AMH levels and duration of infertility between the two main groups. No significant differences in terms of the days of ovarian stimulation, estradiol level in day 8, total gonadotropin dose, number of oocytes retrieved, available embryos and blastocysts, number of embryos transferred nor in rates of fertilization, implantation, clinical pregnancy, live birth and abortion rate between two main groups were found. The only statistically significant difference among the groups with different anti-TPO antibodies levels was found in basal FSH concentration and BMI. Among the clinical outcomes of IVF with respect to the different anti-TPO levels, the only significant difference was found for the number of oocytes retrieved. Analysis of the baseline parameters in relationship to age categories and AMH levels found significant differences between women positive and negative for thyroid antibodies with respect to basal FSH and LH levels for women >37 years and for basal FSH in AMH <0.6 subgroup. CONCLUSIONS: The present study reveals that patients with anti-TPO antibodies showed no significant differences in fertilization, implantation, pregnancy rates, live birth rates and no higher risk for miscarriage following IVF-ET when compared with those negative for anti-thyroid antibodies.
