scholarly journals REDUCTION OF SLOW–FAST PERIODIC SYSTEMS WITH APPLICATIONS TO POPULATION DYNAMICS MODELS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250025 ◽  
Author(s):  
M. MARVÁ ◽  
J.-C. POGGIALE ◽  
R. BRAVO DE LA PARRA

This work deals with the approximate reduction of a nonautonomous two time scales ordinary differential equations system with periodic fast dynamics. We illustrate this technique with the analysis of two models belonging to different fields in ecology. On the one hand, we deal with a two patches periodic predator–prey model with a refuge for prey. Considering migrations between patches to be faster than local interaction allows us to study a three-dimensional system by means of a two-dimensional one. On the other hand, a two time scales periodic eco-epidemic model is addressed by considering two competing species, one of them being affected by a periodic SIR epidemic process which is faster than inter-species interactions. The difference between time scales allows us to study the asymptotic behavior of the four-dimensional system by means of a planar, reduced one. Furthermore, we propose a methodology straightforwardly applicable to a very large class of two time scales periodic systems.

2014 ◽  
Vol 31 (10) ◽  
pp. 2078-2087 ◽  
Author(s):  
Michael L. Larsen ◽  
Clarissa A. Briner ◽  
Philip Boehner

Abstract The spatial positions of individual aerosol particles, cloud droplets, or raindrops can be modeled as a point processes in three dimensions. Characterization of three-dimensional point processes often involves the calculation or estimation of the radial distribution function (RDF) and/or the pair-correlation function (PCF) for the system. Sampling these three-dimensional systems is often impractical, however, and, consequently, these three-dimensional systems are directly measured by probing the system along a one-dimensional transect through the volume (e.g., an aircraft-mounted cloud probe measuring a thin horizontal “skewer” through a cloud). The measured RDF and PCF of these one-dimensional transects are related to (but not, in general, equal to) the RDF/PCF of the intrinsic three-dimensional systems from which the sample was taken. Previous work examined the formal mathematical relationship between the statistics of the intrinsic three-dimensional system and the one-dimensional transect; this study extends the previous work within the context of realistic sampling variability. Natural sampling variability is found to constrain substantially the usefulness of applying previous theoretical relationships. Implications for future sampling strategies are discussed.


2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoqing Wen ◽  
Yue Chen ◽  
Hongwei Yin

We study a three-dimensional system of a diffusive predator-prey model including disease spread for prey and with Dirichlet boundary condition and Michaelis-Menten functional response. By semigroup method, we are able to achieve existence of a global solution of this system. Extinction of this system is established by spectral method. By using bifurcation theory and fixed point index theory, we obtain existence and nonexistence of inhomogeneous positive solutions of this system in steady state.


Author(s):  
Regine Claßen-Bockhoff ◽  
Doris Franke ◽  
Hansjörg Krähmer

Abstract Understanding vascular bundle systems in angiosperms is a challenge. On the one hand, the vascular tissue is extremely important in reconstructing the evolution and survivability of plants, but on the other hand, it forms a complicated three-dimensional system of controversially discussed phylogenetic and ontogenetic origin. To increase clarity, in this paper we briefly summarize histological, phylogenetic and molecular aspects of primary vascular bundle formation in angiosperms, adding histological data on early stages of vascular bundle formation, proposing a concept combining the different views and providing simplified illustrations to improve the understanding of primary vascular systems in angiosperms. Based on the auxin hypothesis, vascular bundle formation is stimulated by the development of leaf primordia. Provascular domains appear at the base of the leaf primordia and develop into two directions (leaf, internode). The low vs. high number of internodal bundles, their circular vs. scattered arrangement and the open vs. closed bundle construction in eudicots vs. monocots can be deduced to be due to processes below the shoot apical meristem. The most important processes distinguishing monocots from eudicots are the isolated bundle initiation outside the primary meristem, the enormous expansion of the leaf bases associated with a high number of vascular bundles and the early onset of primary thickening passively dislocating vascular bundles.


2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ruiqing Shi ◽  
Junmei Qi ◽  
Sanyi Tang

We propose a two-dimensional predatory-prey model with discrete and distributed delay. By the use of a new variable, the original two-dimensional system transforms into an equivalent three-dimensional system. Firstly, we study the existence and local stability of equilibria of the new system. And, by choosing the time delayτas a bifurcation parameter, we show that Hopf bifurcation can occur as the time delayτpasses through some critical values. Secondly, by the use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation. At last, an example with numerical simulations is provided to verify the theoretical results. In addition, some simple discussion is also presented.


2021 ◽  
Vol 13 (1-2) ◽  
pp. 357-376
Author(s):  
Marat Gorodezky ◽  

The article considers creationism as a historically relevant principle in the scientific and philosophic aspects denoting the ontological structure of the world. Outside of the religious interpretation, the author speaks of the dialectics of creation, which is revealed as an implicative connection of the one and nothing. Logical inversion (logical turn), acting from within this implicative connection, is postulated as the principle of a fundamental negation, which, according to the author, forms the true and dramatic essence of the world as a creation. The author distances himself from the widespread discussion between evolutionism and scientific creationism, stating that it does not correspond to the very subject of creationism, understood as the implication of a real from nothing. The author focuses on considering ‘nothing’ as a purely dialectical / metaphysical principle and relies partly on the Hegel’s dialectic of ‘being’ and ‘nothing’, and partly on the neoplatonic concept of the one. Rejecting the medieval interpretation of the temporal beginning and the Hegel’s identity, he deduces a scheme of the logical connection between the one and the difference, which postulates the inversion (turnover) forming the creation - the one and the difference disjunctively change places, the one becomes the real, and the difference out of the one becomes nothing. It is argued that this postulate, in particular, refutes the thesis about the ‘fall into sin’. In the second part of the article, a spatial-phenomenological hypothesis is presented: the author provides a description of the space as a geometrical-semantic plane (projective structure). This hypothesis follows from the phenomenological problem of the duality of a geometric object, which results in the problem of ontological transition between a point and a line (in the aporia of the Eleats) and the related problem of spatial congruence / parallelism. According to the author, the potential for solving these not essentially mathematical, but metaphysical questions is the projective geometry, in which parallel lines intersect at ‘point at infinity’, and space is complemented by the ‘plane at infinity’. The essence of the solution consists, firstly, in the assumption of the single plane, which underlies the transition, and secondly, in the description of the perceived world as a result of a specific turn over and closure of this plane, forming the projective structure. The key in this part is the demonstration of the surface of a three-dimensional object as a phenomenon of perceptual-semantic unfolding, which can be imagined as an action of consciousness, consistently reducing the usual scheme. An important aspect of considering the projective structure is the correlation with ‘the Plane’ by G. Deleuze. The general idea of the article is that the dialectical scheme of creation and the projective structure of the space coincide: the logical inversion (logical turn), acting in connection of the one and nothing, and projective structural turnover – are the same things.


2013 ◽  
Vol 69 (12) ◽  
pp. 1488-1493 ◽  
Author(s):  
Yan-Fei Liu ◽  
Chao-Wei Zhao ◽  
Jian-Ping Ma ◽  
Qi-Kui Liu ◽  
Yu-Bin Dong

Two novel symmetric fluorene-based ligands, namely, 2,7-bis(1H-imidazol-1-yl)-9,9-dimethyl-9H-fluorene [L1 or (I), C21H18N4] and 2,7-bis(1H-imidazol-1-yl)-9,9-dipropyl-9H-fluorene (L2), have been used to construct the coordination polymerscatena-poly[[dichloridodicopper(I)(Cu—Cu)]-μ-2,7-bis(1H-imidazol-1-yl)-9,9-dimethyl-9H-fluorene], [Cu2Cl2(C21H18N4)]n, (II), andcatena-poly[[tetra-μ2-chlorido-tetracopper(I)]-bis[μ-2,7-bis(1H-imidazol-1-yl)-9,9-dipropyl-9H-fluorene]], [Cu4Cl4(C25H26N4)2]n, (III). There are three types of C—H...N hydrogen bonds in (I), resulting a two-dimensional network in theabplane, including a chiral helical chain along thebaxis. Compounds (II) and (III) are related one-dimensional polymers. In both, CuIatoms connect the symmetric ligands (L1 orL2) into a one-dimensional chain. In (II), the {[CuICl2]−} unit, acting as a co-anion, adheres to the one-dimensional chain through a weak Cu...Cu interaction. However, in (III), the {[CuI2Cl4]2−} unit links two different chains into a one-dimensional rope-ladder-type chain. In addition, there are C—H...Cl hydrogen bonds and π–π interactions in the extended structures of (II) and (III), the difference is that the chains in (II) are linked into a two-dimensional network while the chains in (III) are stacked into a three-dimensional framework.


2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Ruiqing Shi ◽  
Junmei Qi ◽  
Sanyi Tang

We propose a three-dimensional stage-structured predatory-prey model with discrete and distributed delays. By use of a new variable, the original three-dimensional system transforms into an equivalent four-dimensional system. Firstly, we study the existence and local stability of positive equilibrium of the new system. And, by choosing the time delayτas a bifurcation parameter, we show that Hopf bifurcation may occur as the time delayτpasses through some critical values. Secondly, by use of normal form theory and central manifold argument, we establish the direction and stability of Hopf bifurcation. At last, some simple discussion is presented.


Author(s):  
Stefano Berretti ◽  
Alberto Del Bimbo ◽  
Pietro Pala ◽  
Francisco Josè Silva Mata

This chapter has a twofold objective. On the one hand, an original approach based on the computation of radial geodesic distances (RGD) is proposed to represent two-dimensional (2D) face images and three-dimensional (3D) face models for the purpose of face recognition. In 3D, the RGD of a generic point of a 3D face surface is computed as the length of the particular geodesic that connects the point with a reference point along a radial direction. In 2D, the RGD of a face image pixel with respect to a reference pixel accounts for the difference of gray level intensities of the two pixels and the Euclidean distance between them. The main contribution of this solution is to permit direct comparison between representations extracted from 2D and 3D facial data, thus opening the way to hybrid approaches for face recognition capable to combine and exploit advantages of different media so as to overcome limitations of traditional solutions based on 2D still images. On the other hand, face representations based on RGDs are used for the purpose of face identification by using them in an operative framework that exploits state of the art techniques for manifold embedding and machine learning. Due to the high dimensionality of face representations based on RGD, embedding into lower-dimensional spaces using manifold learning is applied before classification. Support Vector Machines (SVMs) are used to perform face recognition using 2D- and 3D-RGDs. This shows a general work flow that is not limited to face recognition applications, but can be used in many different contexts of recognition and retrieval. Experimental results are reported for 3D-3D and 2D-3D face recognition using the proposed approach.


1985 ◽  
Vol 107 (2) ◽  
pp. 308-314 ◽  
Author(s):  
I. K. Jennions ◽  
P. Stow

The purpose of this work has been to develop a quasi-three-dimensional blade design and analysis system. In Part II of the paper the computerized blade design system is presented and an example given to illustrate its use. The system comprises a streamline curvature throughflow program incorporating the analysis of Part I of this paper, a blade section stacking program, and one of a number of blade-to-blade calculation programs. The information flow between each part of the system is described and the importance of each stage in the calculation indicated. Information is transferred between programs via a data base which enables other design programs, e.g., heat transfer programs, to access the results. This modular approach enables individual design program advances to be made relatively easily. The system is flexible enough to incorporate a number of blade-to-blade programs, the one used depending on the specific application. An example of the flow through a turbine nozzle guide vane is presented. Experimental data are compared with the results from the quasi-three-dimensional system, a fully three-dimensional program and an unlinked two-dimensional system. The results from the quasi-three-dimensional system are very encouraging.


Author(s):  
Kenneth H. Downing

Three-dimensional structures of a number of samples have been determined by electron crystallography. The procedures used in this work include recording images of fairly large areas of a specimen at high tilt angles. There is then a large defocus ramp across the image, and parts of the image are far out of focus. In the regions where the defocus is large, the contrast transfer function (CTF) varies rapidly across the image, especially at high resolution. Not only is the CTF then difficult to determine with sufficient accuracy to correct properly, but the image contrast is reduced by envelope functions which tend toward a low value at high defocus.We have combined computer control of the electron microscope with spot-scan imaging in order to eliminate most of the defocus ramp and its effects in the images of tilted specimens. In recording the spot-scan image, the beam is scanned along rows that are parallel to the tilt axis, so that along each row of spots the focus is constant. Between scan rows, the objective lens current is changed to correct for the difference in specimen height from one scan to the next.


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