Codimension 2 bifurcation of twisted double homoclinic loops

AbstractA local active coordinates approach is employed to obtain bifurcation equations of twisted double homoclinic loops. Under the condition of one twisted orbit, we obtain the existence and uniqueness and of the 1–1 double homoclinic loop, 2–1 double homoclinic loop, 2–1 right homoclinic loop, 1–1 large homoclinic loop, 2–1 large homoclinic loop and 2–1 large period orbit. For the case of double twisted orbits, we obtain the existence or non-existence of 1–1 double homoclinic loop, 1–2 double homoclinic loop, 2–1 double homoclinic loop, 2–2 double homoclinic loop, 2–1 large homoclinic loop, 1–2 large homoclinic loop, 2–2 large homoclinic loop, 2–2 right homoclinic loop, 2–2 large homoclinic loop, 2–2 left homoclinic loop and 2–2 large period orbit. Moreover, the bifurcation surfaces and their existence regions are given. Besides, bifurcation sets are presented on the 2 dimensional subspace spanned by the first two Melnikov vectors

Codimension 3 bifurcation from orbit-flip homoclinic orbit of weak type

This article is devoted to the research of a new codimension 3 homoclinic orbit bifurcation, which is the orbit-flip of weak type. Such kind of homoclinic orbit is a degenerate case of the orbit-flip homoclinic orbit. We show the existence of 1-homoclinic orbit, 1-periodic orbit, $2^n$-homoclinic orbit and $2^n$-periodic orbit for arbitrary integer $n$. Our strategy is based on the local moving coordinates method

Adsorption Behaviors of 17 -Ethinylestradiol in Sediment-Water System in Northern Taihu Lake, China

Adsorption behavior of 17 -ethinylestradiol (EE2) in northern Taihu Lake sediment was analyzed by using batch equilibrium experiment. Freundlich isotherm could describe the adsorption thermodynamic behavior of EE2 in sediment. Sediment organic matter (SOM) contents had important impacts on the adsorption capacity for EE2. The pH values also influenced the adsorption capacity for EE2. Increase of pH value could decrease the EE2 adsorption, which might be due to the electrostatic repulsion between the anionic form of EE2 and sediments with negative charge under high pH values. Competitive effects of bisphenol A (BPA) on EE2 adsorption were further analyzed. The results showed that low concentration BPA did not have significant influences on EE2 adsorption. However, high concentration BPA could reduce EE2 adsorption, which might be due to the similar molecular diameter of BPA with adsorption sites and one more benzene ring with a hydroxyl group in BPA. These results provide primary information of EE2 adsorption in sediment-water system in Taihu Lake, which is useful for the environmental risk assessment and management of EE2 in studied area

Adsorption Behaviors of 17 α

Adsorption behavior of 17α-ethinylestradiol (EE2) in northern Taihu Lake sediment was analyzed by using batch equilibrium experiment. Freundlich isotherm could describe the adsorption thermodynamic behavior of EE2 in sediment. Sediment organic matter (SOM) contents had important impacts on the adsorption capacity for EE2. The pH values also influenced the adsorption capacity for EE2. Increase of pH value could decrease the EE2 adsorption, which might be due to the electrostatic repulsion between the anionic form of EE2 and sediments with negative charge under high pH values. Competitive effects of bisphenol A (BPA) on EE2 adsorption were further analyzed. The results showed that low concentration BPA did not have significant influences on EE2 adsorption. However, high concentration BPA could reduce EE2 adsorption, which might be due to the similar molecular diameter of BPA with adsorption sites and one more benzene ring with a hydroxyl group in BPA. These results provide primary information of EE2 adsorption in sediment-water system in Taihu Lake, which is useful for the environmental risk assessment and management of EE2 in studied area

Ubiquitous conservative interaction patterns between post-spliced introns and their mRNAs revealed by genome-wide interspecies comparison

Introns, as important vectors of biological functions, can influence many stages of mRNA metabolism. However, in recent research, post-spliced introns are rarely considered. In this study, the optimal matched regions between introns and their mRNAs in nine model organism genomes were investigated with improved Smith–Waterman local alignment software. Our results showed that the distributions of mRNA optimal matched frequencies were highly consistent or universal. There are optimal matched frequency peaks in the UTR regions, which are obvious, especially in the 3′-UTR. The matched frequencies are relatively low in the CDS regions of the mRNA. The distributions of the optimal matched frequencies around the functional sites are also remarkably changed. The centers of the GC content distributions for different sequences are different. The matched rate distributions are highly consistent and are located mainly between 60% and 80%. The most probable value of the optimal matched segments is about 20 bp for lower eukaryotes and 30 bp for higher eukaryotes. These results show that there are abundant functional units in the introns, and these functional units are correlated structurally with all kinds of sequences of mRNA. The interaction between the post-spliced introns and their corresponding mRNAs may play a key role in gene expression

Toward the development of smart capabilities for understanding seafloor stretching morphology and biogeographic patterns via DenseNet from high-resolution multibeam bathymetric surveys for underwater vehicles

The increasing use of underwater vehicles facilitates deep-sea exploration at a wide range of depths and spatial scales. In this paper, we make an initial attempt to develop online computing strategies to identify seafloor categories and predict biogeographic patterns with a deep learning-based architecture, DenseNet, integrated with joint morphological cues, with the expectation of potentially developing its embedded smart capacities. We utilized high-resolution multibeam bathymetric measurements derived from MBES and denoted a collection of joint morphological cues to help with semantic mapping and localization. We systematically strengthened dominant feature propagation and promoted feature reuse via DenseNet by applying the channel attention module and spatial pyramid pooling. From our experiment results, the seafloor classification accuracy reached up to 89.87%, 82.01%, and 73.52% on average in terms of PA, MPA, and MIoU metrics, achieving comparable performances with the state-of-the-art deep learning frameworks. We made a preliminary study on potential biogeographic distribution statistics, which allowed us to delicately distinguish the functionality of probable submarine benthic habitats. This study demonstrates the premise of using underwater vehicles through unbiased means or pre-programmed path planning to quantify and estimate seafloor categories and the exhibited fine-scale biogeographic patterns

Stochastic stability, random attractor and homoclinic and heteroclinic bifurcation

Cette thèse est consacré à l'étude de certaines équations différentielles stochastiques et la bifurcation des orbites homocline et hétérocline. On présente les conditions pour la stabilité stochastique du modèle SIRS stochastique avec ou sans retard. Nous montrons que l'équation stochastique de Ginzburg-Landau avec perturbation aléatoire additive possède un unique D-attracteur aléatoire dans l'espace entier. Dans la seconde partie, en utilisant la méthode de repère mobile, on étudie la bifurcation dans trois cas de figure: la bifurcation d'orbite homocline non résonante en dimension 3 avec inclination-flip, la bifurcation d'orbites homocline doubles tordues de codimension 2, et la bifurcation de cycle hétérodimensionnel dégénéré avec orbite-flip. Dans le premier cas nous montrons, pour le système perturbé, l'existence d'orbite 1-homocline, orbite 1-périodique, orbite 2n-homocline et orbite 2n-périodique. Dans le deuxieme cas, on montre des résultats de bifurcation sous la condition d'une orbite tordue ou les deux tordues. Dans le troisième situation, sous des hypothèses génériques, nous présentons des conditions pour l'existence, unicité, co-existence ou non-co-existence d'orbite homocline, d'orbite heterocline et d'orbite périodique. Dans tous les cas les surfaces de bifurcation sont obtenues et elles sont présentées dans le sous espace de dimension 2 engendré par les deux premiers vecteurs de Melnikov.The thesis is devoted to the study of some stochastic differential equations and homoclinic and heteroclinic bifurcations. We present the stability conditions of the disease-free equilibrium for the stochastic SIRS model with or without distributed time delay. We show that the stochastic Ginzburg-Landau equation with additive noise on the entire n-dimensional space possesses a unique D-random attractor. ln the second part, by employing the moving frame method, we study the bifurcations in three situations: the bifurcation of the non-resonant 3D homoclinic orbit with inclination-fIip, codimension 2 bifurcation of twisted double homoclinic loops, and heterodimensional cycle bifurcation with orbit-flip. ln the first case, we show, for the perturbed systems, the existence of 1-homoclinic orbit, 1-periodic orbit, 2n-homoclinic orbit and 2n-periodic orbit. ln the second case, we obtain bifurcation results both under the condition of one twisted orbit and double twisted orbits. ln the last case, under some generic hypotheses, we present conditions for the existence, uniqueness, coexistence or non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. ln all cases we figure out the bifurcation diagrams based on the existence region and they are presented on the 2-dimensional subspace spanned by the first two Melnikov vectors