scholarly journals Computational methods for global analysis of homoclinic and heteroclinic orbits: A case study

1993 ◽  
Vol 5 (1) ◽  
pp. 37-57 ◽  
Author(s):  
Mark J. Friedman ◽  
Eusebius J. Doedel
Keyword(s):  
Computational Methods ◽  
Global Analysis ◽  
Heteroclinic Orbits ◽  
Homoclinic And Heteroclinic Orbits

scholarly journals Decision-Making Processes in Controlling Exposure to Sunlight Supported by Simulation Tools: A Case Study in Warm Weather

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4100
Author(s):  
Mariana Huskinson ◽  
Antonio Galiano-Garrigós ◽  
Ángel Benigno González-Avilés ◽  
M. Isabel Pérez-Millán
Keyword(s):  
Decision Making ◽  
Global Analysis ◽  
Energy Performance ◽  
Information Modeling ◽  
The European Union ◽  
Evaluation Tool ◽  
Simulation Tools ◽  
Building Information ◽  
The Impact

Improving the energy performance of existing buildings is one of the main strategies defined by the European Union to reduce global energy costs. Amongst the actions to be carried out in buildings to achieve this objective is working with passive measures adapted to each type of climate. To assist designers in the process of finding appropriate solutions for each building and location, different tools have been developed and since the implementation of building information modeling (BIM), it has been possible to perform an analysis of a building’s life cycle from an energy perspective and other types of analysis such as a comfort analysis. In the case of Spain, the first BIM environment tool has been implemented that deals with the global analysis of a building’s behavior and serves as an alternative to previous methods characterized by their lack of both flexibility and information offered to designers. This paper evaluates and compares the official Spanish energy performance evaluation tool (Cypetherm) released in 2018 using a case study involving the installation of sunlight control devices as part of a building refurbishment. It is intended to determine how databases and simplifications affect the designer’s decision-making. Additionally, the yielded energy results are complemented by a comfort analysis to explore the impact of these improvements from a users’ wellbeing viewpoint. At the end of the process the yielded results still confirm that the simulation remains far from reality and that simulation tools can indeed influence the decision-making process.

scholarly journals A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Jingjing Feng ◽  
Qichang Zhang ◽  
Wei Wang ◽  
Shuying Hao
Keyword(s):  
Dynamic Systems ◽  
Approximation Method ◽  
Padé Approximation ◽  
Global Bifurcation ◽  
Heteroclinic Orbits ◽  
Symmetric System ◽  
Pade Approximation ◽  
New Approach ◽  
Homoclinic And Heteroclinic Orbits ◽  
Single Orbit

In dynamic systems, some nonlinearities generate special connection problems of non-Z2symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z2symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z2symmetric nonlinear quintic systems (orbit with one cusp); and Z2symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.

More Dynamical Properties Revealed from a 3D Lorenz-like System

2014 ◽  
Vol 24 (10) ◽  
pp. 1450133 ◽  
Author(s):  
Haijun Wang ◽  
Xianyi Li
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Heteroclinic Orbits ◽  
Mathematical Work ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Homoclinic And Heteroclinic Orbits ◽  
Dynamical Properties ◽  
Theoretical Results

After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0. All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means — both "locally" and "globally" and both "finitely" and "infinitely" — to comprehensively explore a given system.

Digital Historicism and the Historicity of Digital Texts

2019 ◽  
pp. 66-100
Author(s):  
James E. Dobson
Keyword(s):  
Text Mining ◽  
Computational Methods ◽  
Historical Research ◽  
Affective Content ◽  
Digital Texts ◽  
Sentiment Mining ◽  
Interpretive Framework

This chapter takes up several important theoretical problems and complexities introduced by text mining and datafication to historiography and historical research in order to think about the problems and promises of a digital historicism. The chapter argues for an approach that takes the historicity of the digitized archive seriously without reducing the use of computational methods to either those framed strictly by the terms and language of the present or to a form of rigid historicism that would require enclosing the archive in synchronically constructed interpretive framework. Many of the approaches used within text mining deploy secondary archives—dictionaries, thesauruses, and other forms of human-constructed schemata—that have tended to capture categories used in the present. The chapter concludes by examining the methods and practice of extracting and analyzing emotional or affective content in texts through what is called sentiment mining. Functioning as a case study, sentiment mining demonstrates the need for quantitative and computational humanists to give more attention to the historical dimensions of both text and affect, to both primary and secondary digital sources.

scholarly journals The New Set Up of Local Performance Indices into WaterNetGen and Application to Santarém’s Network

2020 ◽  
Vol 2 (1) ◽  
pp. 18 ◽  
Author(s):  
Marco Amos Bonora ◽  
Fabio Caldarola ◽  
Mario Maiolo ◽  
Joao Muranho ◽  
Joaquim Sousa
Keyword(s):  
Water Distribution ◽  
Global Analysis ◽  
Distribution Network ◽  
Water Distribution Network ◽  
Mathematical Framework ◽  
Water Networks ◽  
Performance Indices ◽  
Set Up ◽  
Pressure Driven Analysis

A new set of local performance indices has recently been introduced within a mathematical framework specifically designed to promote a local–global analysis of water networks. Successively, some local indices were also set up and implemented on WaterNetGen to better exploit their potential. In this paper, after a very brief overview of tools and main notations, Santarém’s (Portugal) water distribution network (WDN) is examined, applying to it the mentioned set of local indices, as a new real case study. The paper also focuses on the Hypotesis required to assess these indices in a pressure driven analysis (PDA) approach, analyzing and discussing the results obtained from such a simulation.

scholarly journals SINGULAR ORBITS AND DYNAMICS AT INFINITY OF A CONJUGATE LORENZ-LIKE SYSTEM

2015 ◽  
Vol 20 (2) ◽  
pp. 148-167 ◽  
Author(s):  
Fengjie Geng ◽  
Xianyi Li
Keyword(s):  
Theoretical Analysis ◽  
Lyapunov Exponents ◽  
Heteroclinic Orbits ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Basic Properties ◽  
Homoclinic And Heteroclinic Orbits ◽  
Quadratic Nonlinearities ◽  
Singular Orbits

A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations are investigated by some numerical and theoretical analysis. The forming mechanisms of compound structures of its new chaotic attractors obtained by merging together two simple attractors after performing one mirror operation are also presented. Furthermore, some of its other complex dynamical behaviours, which include the existence of singularly degenerate heteroclinic cycles, the existence of homoclinic and heteroclinic orbits and the dynamics at infinity, etc, are formulated in detail. In the meantime, some problems deserving further investigations are presented.

scholarly journals Computational Methods for the Identification of Molecular Targets of Toxic Food Additives. Butylated Hydroxytoluene as a Case Study

Molecules ◽  
2020 ◽  
Vol 25 (9) ◽  
pp. 2229 ◽  
Author(s):  
Valentina Tortosa ◽  
Valentina Pietropaolo ◽  
Valentina Brandi ◽  
Gabriele Macari ◽  
Andrea Pasquadibisceglie ◽  
...  
Keyword(s):  
Computational Methods ◽  
Food Additives ◽  
Daily Intake ◽  
Experimental Studies ◽  
Butylated Hydroxytoluene ◽  
Computational Techniques ◽  
Toxicological Effects ◽  
Ligand Interactions ◽  
Toxic Food

Butylated hydroxytoluene (BHT) is one of the most commonly used synthetic antioxidants in food, cosmetic, pharmaceutical and petrochemical products. BHT is considered safe for human health; however, its widespread use together with the potential toxicological effects have increased consumers concern about the use of this synthetic food additive. In addition, the estimated daily intake of BHT has been demonstrated to exceed the recommended acceptable threshold. In the present work, using BHT as a case study, the usefulness of computational techniques, such as reverse screening and molecular docking, in identifying protein–ligand interactions of food additives at the bases of their toxicological effects has been probed. The computational methods here employed have been useful for the identification of several potential unknown targets of BHT, suggesting a possible explanation for its toxic effects. In silico analyses can be employed to identify new macromolecular targets of synthetic food additives and to explore their functional mechanisms or side effects. Noteworthy, this could be important for the cases in which there is an evident lack of experimental studies, as is the case for BHT.

scholarly journals LDAI-ISPS: LncRNA–Disease Associations Inference Based on Integrated Space Projection Scores

2020 ◽  
Vol 21 (4) ◽  
pp. 1508
Author(s):  
Yi Zhang ◽  
Min Chen ◽  
Ang Li ◽  
Xiaohui Cheng ◽  
Hong Jin ◽  
...  
Keyword(s):  
Computational Methods ◽  
Area Under The Curve ◽  
Predictive Performance ◽  
Weighted Networks ◽  
Disease Associations ◽  
Space Projection ◽  
Auc Value ◽  
Leave One Out ◽  
Key Steps

Long non-coding RNAs (long ncRNAs, lncRNAs) of all kinds have been implicated in a range of cell developmental processes and diseases, while they are not translated into proteins. Inferring diseases associated lncRNAs by computational methods can be helpful to understand the pathogenesis of diseases, but those current computational methods still have not achieved remarkable predictive performance: such as the inaccurate construction of similarity networks and inadequate numbers of known lncRNA–disease associations. In this research, we proposed a lncRNA–disease associations inference based on integrated space projection scores (LDAI-ISPS) composed of the following key steps: changing the Boolean network of known lncRNA–disease associations into the weighted networks via combining all the global information (e.g., disease semantic similarities, lncRNA functional similarities, and known lncRNA–disease associations); obtaining the space projection scores via vector projections of the weighted networks to form the final prediction scores without biases. The leave-one-out cross validation (LOOCV) results showed that, compared with other methods, LDAI-ISPS had a higher accuracy with area-under-the-curve (AUC) value of 0.9154 for inferring diseases, with AUC value of 0.8865 for inferring new lncRNAs (whose associations related to diseases are unknown), with AUC value of 0.7518 for inferring isolated diseases (whose associations related to lncRNAs are unknown). A case study also confirmed the predictive performance of LDAI-ISPS as a helper for traditional biological experiments in inferring the potential LncRNA–disease associations and isolated diseases.

HOMOCLINIC AND HETEROCLINIC ORBITS AND BIFURCATIONS OF A NEW LORENZ-TYPE SYSTEM

2011 ◽  
Vol 21 (09) ◽  
pp. 2695-2712 ◽  
Author(s):  
XIANYI LI ◽  
HAIJUN WANG
Keyword(s):  
Chaotic Attractor ◽  
Lorenz System ◽  
Type System ◽  
Pitchfork Bifurcation ◽  
Heteroclinic Orbits ◽  
Chen System ◽  
Homoclinic And Heteroclinic Orbits ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
The Stability

In this paper, a new Lorenz-type system with chaotic attractor is formulated. The structure of the chaotic attractor in this new system is found to be completely different from that in the Lorenz system or the Chen system or the Lü system, etc., which motivates us to further study in detail its complicated dynamical behaviors, such as the number of its equilibrium, the stability of the hyperbolic and nonhyperbolic equilibrium, the degenerate pitchfork bifurcation, the Hopf bifurcation and the local manifold character, etc., when its parameters vary in their space. The existence or nonexistence of homoclinic and heteroclinic orbits of this system is also rigorously proved. Numerical simulation evidences are also presented to examine the corresponding theoretical analytical results.

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