PERIODIC PERTURBATION of QUADRATIC SYSTEMS WITH TWO INFINITE HETEROCLINIC CYCLES

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences

In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.

Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the evolution of harming and recognition in finite panmictic and infinite structured populations.

Natural selection may favor two very different types of social behaviors that have costs in vital rates (fecundity and/or survival) to the actor: helping behaviors, which increase the vital rates of recipients, and harming behaviors, which reduce the vital rates of recipients. Although social evolutionary theory has mainly dealt with helping behaviors, competition for limited resources creates ecological conditions in which an actor may benefit from expressing behaviors that reduce the vital rates of neighbors. This may occur if the reduction in vital rates decreases the intensity of competition experienced by the actor or that experienced by its offspring. Here, we explore the joint evolution of neutral recognition markers and marker-based costly conditional harming whereby actors express harming, conditional on actor and recipient bearing different conspicuous markers. We do so for two complementary demographic scenarios: finite panmictic and infinite structured populations. We find that marker-based conditional harming can evolve under a large range of recombination rates and group sizes under both finite panmictic and infinite structured populations. A direct comparison with results for the evolution of marker-based conditional helping reveals that, if everything else is equal, marker-based conditional harming is often more likely to evolve than marker-based conditional helping.

Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the Lorenz system

In this paper, by using the Poincare compactification in R(3) we make a global analysis of the Lorenz system, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques we show that for the parameter value b = 0 the system presents an infinite set of singularly degenerate heteroclinic cycles, which consist of invariant sets formed by a line of equilibria together with heteroclinic orbits connecting two of the equilibria. The dynamical consequences related to the existence of such cycles are discussed. In particular a possibly new mechanism behind the creation of Lorenz-like chaotic attractors, consisting of the change in the stability index of the saddle at the origin as the parameter b crosses the null value, is proposed. Based on the knowledge of this mechanism we have numerically found chaotic attractors for the Lorenz system in the case of small b > 0, so nearby the singularly degenerate heteroclinic cycles.

Net power optimization of an irreversible Otto cycle using ECOP and ecological function

This paper presents an analysis of an irreversible Otto cycle aiming to optimize the net power through ECOP and ecological function. The studied cycle operates between two thermal reservoirs of infinite thermal capacity, with internal irreversibilities derived from non-isentropic behavior of compression and expansion processes, irreversibilities from thermal resistance in heat exchangers and heat leakage from the high temperature reservoir to the low temperature reservoir. Analytical expressions are applied for the power outputs optimized by the ECOP, by the ecological function and by the maximum power criteria, in conjunction with a graphic analysis, in which some cycle operation parameters are analyzed for an increased comprehension of the effects of the irreversibilities in the optimized power.

Interplay Between Cell Growth And Cell Cycle In Plants.

The growth of organs and whole plants depends on both cell growth and cell-cycle progression, but the interaction between both processes is poorly understood. In plants, the balance between growth and cell-cycle progression requires coordinated regulation of four different processes: macromolecular synthesis (cytoplasmic growth), turgor-driven cell-wall extension, mitotic cycle, and endocycle. Potential feedbacks between these processes include a cell-size checkpoint operating before DNA synthesis and a link between DNA contents and maximum cell size. In addition, key intercellular signals and growth regulatory genes appear to target at the same time cell-cycle and cell-growth functions. For example, auxin, gibberellin, and brassinosteroid all have parallel links to cell-cycle progression (through S-phase Cyclin D-CDK and the anaphase-promoting complex) and cell-wall functions (through cell-wall extensibility or microtubule dynamics). Another intercellular signal mediated by microtubule dynamics is the mechanical stress caused by growth of interconnected cells. Superimposed on developmental controls, sugar signalling through the TOR pathway has recently emerged as a central control point linking cytoplasmic growth, cell-cycle and cell-wall functions. Recent progress in quantitative imaging and computational modelling will facilitate analysis of the multiple interconnections between plant cell growth and cell cycle and ultimately will be required for the predictive manipulation of plant growth.

Screening The Life Cycle Of Schistosoma Mansoni Using High-resolution Mass Spectrometry.

Schistosomiasis is a common tropical disease caused by Schistosoma species Schistosomiasis' pathogenesis is known to vary according to the worms' strain. Moreover, high parasitical virulence is directly related to eggs release and granulomatous inflammation in the host's organs. This virulence might be influenced by different classes of molecules, such as lipids. Therefore, better understanding of the metabolic profile of these organisms is necessary, especially for an increased potential of unraveling strain virulence mechanisms and resistance to existing treatments. In this report, direct-infusion electrospray high-resolution mass spectrometry (ESI(+)-HRMS) along with the lipidomic platform were employed to rapidly characterize and differentiate two Brazilian S. mansoni strains (BH and SE) in three stages of their life cycle: eggs, miracidia and cercariae, with samples from experimental animals (Swiss/SPF mice). Furthermore, urine samples of the infected and uninfected mice were analyzed to assess the possibility of direct diagnosis. All samples were differentiated using multivariate data analysis, PCA, which helped electing markers from distinct lipid classes; phospholipids, diacylglycerols and triacylglycerols, for example, clearly presented different intensities in some stages and strains, as well as in urine samples. This indicates that biochemical characterization of S. mansoni may help narrowing-down the investigation of new therapeutic targets according to strain composition and aggressiveness of disease. Interestingly, lipid profile of infected mice urine varies when compared to control samples, indicating that direct diagnosis of schistosomiasis from urine may be feasible.

Polymorphisms Of Cell Cycle Control Genes Influence The Development Of Sporadic Medullary Thyroid Carcinoma.

The role of key cell cycle regulation genes such as, CDKN1B, CDKN2A, CDKN2B, and CDKN2C in sporadic medullary thyroid carcinoma (s-MTC) is still largely unknown. In order to evaluate the influence of inherited polymorphisms of these genes on the pathogenesis of s-MTC, we used TaqMan SNP genotyping to examine 45 s-MTC patients carefully matched with 98 controls. A multivariate logistic regression analysis demonstrated that CDKN1B and CDKN2A genes were related to s-MTC susceptibility. The rs2066827*GT+GG CDKN1B genotype was more frequent in s-MTC patients (62.22%) than in controls (40.21%), increasing the susceptibility to s-MTC (OR=2.47; 95% CI=1.048-5.833; P=0.038). By contrast, the rs11515*CG+GG of CDKN2A gene was more frequent in the controls (32.65%) than in patients (15.56%), reducing the risk for s-MTC (OR=0.174; 95% CI=0.048-0.627; P=0.0075). A stepwise regression analysis indicated that two genotypes together could explain 11% of the total s-MTC risk. In addition, a relationship was found between disease progression and the presence of alterations in the CDKN1A (rs1801270), CDKN2C (rs12885), and CDKN2B (rs1063192) genes. WT rs1801270 CDKN1A patients presented extrathyroidal tumor extension more frequently (92%) than polymorphic CDKN1A rs1801270 patients (50%; P=0.0376). Patients with the WT CDKN2C gene (rs12885) presented larger tumors (2.9±1.8 cm) than polymorphic patients (1.5±0.7 cm; P=0.0324). On the other hand, patients with the polymorphic CDKN2B gene (rs1063192) presented distant metastases (36.3%; P=0.0261). In summary, we demonstrated that CDKN1B and CDKN2A genes are associated with susceptibility, whereas the inherited genetic profile of CDKN1A, CDKN2B, and CDKN2C is associated with aggressive features of tumors. This study suggests that profiling cell cycle genes may help define the risk and characterize s-MTC aggressiveness.

Glycosaminoglycan distribution in the rat uterine cervix during the estrous cycle

OBJECTIVE: To analyze the amount of glycosaminoglycans in the uterine cervix during each phase of the rat estrous cycle. DESIGN: Based on vaginal smears, forty female, regularly cycling rats were divided into four groups (n = 10 for each group): GI - proestrous, GII - estrous, GIII - metaestrous and GIV - diestrous. Animals were sacrificed at each phase of the cycle, and the cervix was immediately removed and submitted to biochemical extraction and determination of sulfated glycosaminoglycans and hyaluronic acid. The results were analyzed by ANOVA followed by the Bonferroni post-hoc test. RESULTS: The uterine cervix had the highest amount of total sulfated glycosaminoglycans and dermatan sulfate during the estrous phase (8.90 ± 0.55 mg/g of cetonic extract, p<0.001; and 8.86 ± 0.57 mg/g of cetonic extract, p<0.001). In addition, there was more heparan sulfate at the cervix during the proestrous phase (0.185 ± 0.03 mg/g of cetonic extract) than during any other phase (p<0.001). There were no significant changes in the concentration of hyaluronic acid in the uterine cervix during the estrous cycle. CONCLUSION: Our data suggest that the amount of total sulfated glycosaminoglycans may be influenced by hormonal fluctuations related to the estrous cycle, with dermatan sulfate and heparan sulfate being the glycosaminoglycans most sensitive to hormonal change.

Survival, population pize, and gonotrophic cycle duration of Nyssomyia neivai (Diptera: Psychodidae) at an endemic area of American Cutaneous Leishmaniasis in Southeastern Brazil

The survival, absolute population size, gonotrophic cycle duration, and temporal and spatial abundance of Nyssomyia neivai (Pinto) were studied in a rural area endemic for American cutaneous leishmaniasis (ACL) in Conchal, Sõo Paulo State, southeastern Brazil, using mark-release-recapture techniques and by monitoring population fluctuation. The monthly abundance exhibited a unimodal pattern, with forest and domicile habitats having the highest relative abundances. A total of 1,873 males and 3,557 females were marked and released during the six experiments, of which 4.1-13.0 per cent of males and 4.1-11.8 per cent of females were recaptured. Daily survivorship estimated from the decline in recaptures per day was 0.681 for males and 0.667 for females. Gonotrophic cycle duration was estimated to be 4.0 d. Absolute population size was calculated using the Lincoln Index and ranged from 861 to 4,612 males and from 2,187 to 19,739 females. The low proportion of females that reach the age when they are potentially infective suggests that N. neivai has a low biological capacity to serve as a vector and that factors such as high biting rates and opportunistic feeding behavior would be needed to enable Leishmania (Viannia) braziliensis Vianna transmission. This agreed with the epidemiological pattern of ACL in southeastern Brazil that is characterized by low incidence, with isolated cases acquired principally within domiciliary habitats

Electromagnetic energy within a magnetic infinite cylinder and scattering properties for oblique incidence

We analytically calculate the time-averaged electromagnetic energy stored inside a nondispersive magnetic isotropic cylinder that is obliquely irradiated by an electromagnetic plane wave. An expression for the optical-absorption efficiency in terms of the magnetic internal coefficients is also obtained. In the low absorption limit, we derive a relation between the normalized internal energy and the optical-absorption efficiency that is not affected by the magnetism and the incidence angle. This relation, indeed, seems to be independent of the shape of the scatterer. This universal aspect of the internal energy is connected to the transport velocity and consequently to the diffusion coefficient in the multiple scattering regime. Magnetism favors high internal energy for low size parameter cylinders, which leads to a low diffusion coefficient for electromagnetic propagation in 2D random media. (C) 2010 Optical Society of America

LIFE CYCLE AND POPULATION STRUCTURE OF AEGLA PAULENSIS (DECAPODA: ANOMURA: AEGLIDAE)

We describe growth, longevity, sex ratio, reproductive period, and recruitment of Aegla paulensis from Jaragua Stale Park, Sao Paulo, Brazil (23 degrees 27'27.9 '' S; 46 degrees 45'32.3 '' W). The population was sampled monthly (September 2007 through August 2009) with the aid of traps. Over five thousand individuals were captured, sexed, measured (carapace length = CL) and inspected for reproductive traits (females only), and then released back to the sampling site. The pattern of the reproductive cycle was strongly seasonal (austral mid autumn through late winter), with a single recruitment pulse per year. The obtained von Bertalanffy growth equations were CL = 21.25[1-e(-0.041(t + 1.250))] and CL = 16.52[1-e(-0.049(t + 1.823))] for males and females, respectively. Males (mean CL +/- SD = 11.86 +/- 2.79 mm) attain larger sizes than females (mean CL +/- SD = 10.84 +/- 2.36 mm). Aegla paulensis reproduces twice during an estimated life span of 40.2 months for females and 33.9 months for males. Temporal variation of sex ratio showed a distinctive pattern characterized by a sequence of three distinct periods that repeated from one year to another, and which suggested that a behavioral component influence the proportion of sex in adult specimens sampled with traps during reproductive and non-reproductive periods.