scholarly journals Applications de méthodes d’agrégation de variables à l’analyse de modèles spatiaux de dynamique des populations

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Tri Nguyen-Huu ◽  
Pierre Auger
Keyword(s):  
Population Dynamics ◽  
Time Scales ◽  
Discrete Models ◽  
Global Dynamics ◽  
Dynamique Des Populations ◽  
Simplified Models ◽  
Aggregation Of Variables ◽  
Reduced Models ◽  
International Audience ◽  
Different Time Scales

International audience Models in population dynamics can deal with an important number of parameters and variables, which can make them difficult to analyse. Aggregation of variables allow reducing complexity of such models by building simplified models governing fewer variables by use of the existence of different time scales associated to the processes governing the whole system. Those reduced models allows analysing and describing the global dynamics of the system. We present those methods for time discrete models and illustrate their use for the study of spatial host-parasitoids models. Les modèles de dynamique de populations peuvent prendre en compte un nombre important de paramètres et de variables, ce qui les rend difficiles à analyser. Lorsqu’il existe des processus associés à deux échelles de temps différentes, une lente et une rapide, les méthodes d’agrégation de variables permettent de construire un modèle simplifié qui comporte un nombre plus faible de variables. Elles permettent ainsi d’analyser et de décrire un système de manière globale. Nous présentons ces méthodes dans le cas de modèles discrets, puis nous illustrons leur utilisation à l’aide de modèles hôte-parasitoïdes spatialisés.

POPULATION GROWTH MODELING WITH BOOM AND BUST PATTERNS: THE IMPULSIVE DIFFERENTIAL EQUATION FORMALISM

2015 ◽  
Vol 23 (supp01) ◽  
pp. S135-S149 ◽  
Author(s):  
FERNANDO CÓRDOVA-LEPE ◽  
GONZALO ROBLEDO ◽  
JAVIER CABRERA-VILLEGAS
Keyword(s):  
Differential Equation ◽  
Population Dynamics ◽  
Time Scales ◽  
Chaotic Dynamics ◽  
Impulsive Differential Equation ◽  
Dynamical Behavior ◽  
Single Species ◽  
Open Problems ◽  
Boom And Bust ◽  
Different Time Scales

This note gives an overview on basic mathematical models describing the population dynamics of a single species whose vital dynamics has different time scales. We present five cases combining two time–scales with Malthusian growth in at least one scale. The dynamical behavior shows a progressive complexity, from "naive" to chaotic dynamics (in the Li–Yorke's sense). In addition, some open problems and new results are presented.

scholarly journals La méthode des élucidations successives

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Claude Lobry
Keyword(s):  
Mathematical Model ◽  
Population Dynamics ◽  
Natural Language ◽  
Human Brain ◽  
Formal Language ◽  
Formal Model ◽  
Formal Models ◽  
Dynamique Des Populations ◽  
International Audience ◽  
Modelling Process

International audience In the process of elaboration of a model one emphasize on the necessity of confronting the model with the reality which it is supposed to represent. There is another aspect of the modelling process, to my opinion also essential, about which one usually do not speak. It consists in a logico-linguistic work where formal models are used to produce prediction which are not confronted with the reality but serve for falsifying assertions which nevertheless seemed to be derived from the not formalized model. More exactly a first informal model is described in the natural language and, considered in the natural language, seems to say some thing but in a more or less clear way. Then we translate the informal model into a formal model (mathematical model or computer model) where what was argumentation becomes demonstration.The formal model so serves for raising ambiguities of the natural language. But conversely a too much formalized text quickly loses any sense for a human brain what makes necessary the return for a less formal language. It is these successive "translations" between more or less formal languages that I try to analyze on two examples, the first one in population dynamics, the second in mathematics. Dans le processus d’élaboration d’un modèle on insiste beaucoup sur la nécessité de confronter le modèle à la réalité qu’il est sensé représenter. Il est un autre aspect de la modélisation, à mon avis tout aussi essentiel, dont on ne parle pas. Il s’agit d’un travail logico-linguistique où des modèles formels sont utilisés pour produire des prédiction qui ne sont pas confrontées à la réalité mais servent à falsifier des affirmations qui semblaient pourtant se déduire du modèle. Plus précisément un premier modèle informel est décrit dans la langue naturelle et, toujours dans la langue naturelle, semble dire quelques chose mais de façon plus ou moins claire. Alors on traduit le modèle informel en un modèle formel (mathématique ou informatique) où ce qui était argumentation devient démonstration. Le modèle formel sert ainsi à lever des ambiguïtés de la langue naturelle. Mais inversement un texte trop formalisé perd rapidement tout sens pour un cerveau humain ce qui rend nécessaire le retour à une langue moins formelle. Ce sont ces “traductions" successives entre langues plus ou moins formelles que je cherche à analyser sur deux exemples, le premier en dynamique des populations, le second en mathématiques.

scholarly journals Model Reduction of DFIG Wind Turbine System Based on Inner Coupling Analysis

Energies ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 3234 ◽  
Author(s):  
Pingping Han ◽  
Yu Zhang ◽  
Lei Wang ◽  
Yan Zhang ◽  
Zihao Lin
Keyword(s):  
Wind Turbine ◽  
Time Scales ◽  
Time Scale ◽  
Simplified Model ◽  
Dynamic Processes ◽  
Simplified Models ◽  
Transient Model ◽  
Electromagnetic Transient ◽  
Wind Turbine System ◽  
Different Time Scales

The doubly-fed induction generator (DFIG) wind turbine system, which is composed of the wind turbine, generator, rotor-side converter, grid-side converter, and so on, is a typical multi-time scale system. The dynamic processes at different time scales do not exist in isolation. Furthermore, neglecting the coupling of parameters of different time scales to reduce the order of the model will lead to deviation between the simulation results and the actual results, which may not be suitable for power system transient analysis. This paper proposes an electromechanical transient model and an electromagnetic transient model of the DFIG wind turbine system that consider the interaction of multiple time-scale dynamic processes. Firstly, the paper applies the modal analysis method to explain the multi-time scale characteristics of the DFIG wind turbine system. Secondly, the variation in the eigenvalues of the DFIG wind turbine system before and after the order reduction and the coupling between variables and the system, as well as the coupling between variables of different time scales, are analyzed to obtain the preliminary 21-order simplified model. Thirdly, considering the weak coupling characteristics between the mechanical part and the electromagnetic part of the DFIG wind turbine system, the 21-order simplified model is decomposed into a 15-order electromagnetic transient model and a six-order electromechanical transient model on the basis of their time scales. Then, according to the balance between simulation time and simulation accuracy, the 14-order electromagnetic transient model and the 10 or 12-order electromechanical transient model are finally obtained. Finally, the rationality of the simplified models is verified by simulations under two large disturbance conditions, namely wind speed abrupt change and voltage sag. The obtained simplified models have reference significance for improving the simulation speed of a wind power grid-connected system and analyzing the internal mechanism of the DFIG wind turbine system’s stability.

scholarly journals Existence, stability and controllability results of fractional dynamic system on time scales with application to population dynamics

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Vipin Kumar ◽  
Muslim Malik
Keyword(s):  
Population Dynamics ◽  
Fixed Point ◽  
Dynamic System ◽  
Time Scales ◽  
Existence Of Solutions ◽  
Ulam Stability ◽  
Numerical Examples ◽  
Fractional Dynamic System ◽  
Nonlinear Alternative ◽  
Different Time Scales

AbstractIn this manuscript, we investigate the existence, uniqueness, Hyer-Ulam stability and controllability analysis for a fractional dynamic system on time scales. Mainly, this manuscript has three segments: In the first segment, we give the existence of solutions. The second segment is devoted to the study of stability analysis while in the last segment, we establish the controllability results. We use the Banach and nonlinear alternative Lery-Schauder–type fixed point theorem to establish these results. Also, we give some numerical examples for different time scales. Moreover, we give two applications to outline the effectiveness of these obtained results.

scholarly journals Migrations in the Rosenzweig-MacArthur model and the "atto-fox" problem

2015 ◽  
Vol Volume 20 - 2015 - Special... ◽  
Author(s):  
Claude Lobry ◽  
Tewfik Sari
Keyword(s):  
Population Dynamics ◽  
Limit Cycle ◽  
Differential System ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Dynamique Des Populations ◽  
Predator Prey ◽  
International Audience

International audience The Rosenzweig-MacArthur model is a system of two ODEs used in population dynamics to modelize the predator-prey relationship. For certain values of the parameters the differential system exhibits a unique stable limit cycle. When the dynamics of the prey is faster than the dynamics of the predator, during oscillations along the limit cycle, the density of preys take so small values that it cannot modelize any actual population. This phenomenon is known as the "atto-fox" problem. In this paper we assume that the populations are living in two patches and are able to migrate from one patch to another. We give conditions for which the migration can prevent the density of prey being too small. Le modèle de Rosenzweig-MacArthur est un système de deux équations différentielles utilisé en dynamique des populations pour modéliser la relation entre un prédateur et sa proie. Pour certaines valeurs des paramètres le système différentiel possède un cycle limite unique stable. Lorsque la dynamique de la proie est plus rapide que celle du prédateur, durant les oscillations le long du cycle, la densité des proies atteint des valeurs tellement petites qu'elle ne peut modéliser une situation issue du monde réel. Ce phénomène est connu sous le nom du problème "atto-fox". Dans cet article on suppose que les populations sont réparties entre deux patches et qu'elles peuvent migrer de l'un à l'autre. Nous donnons des conditions qui assurent que la migration va empêcher la densité des proies de devenir trop petite.

Linear discrete models with different time scales

1995 ◽  
Vol 43 (4) ◽  
pp. 465-476 ◽  
Author(s):  
Eva Sánchez ◽  
Rafael Bravo de la Parra ◽  
Pierre Auger
Keyword(s):  
Time Scales ◽  
Discrete Models ◽  
Different Time Scales

Agent-Based Computational Model

2017 ◽  
Author(s):  
Joshua M. Epstein
Keyword(s):  
Computational Model ◽  
Bounded Rationality ◽  
Time Scales ◽  
Spatially Explicit ◽  
Agent Based ◽  
Affective Component ◽  
Elementary Type ◽  
Social Component ◽  
Different Time Scales

This part describes the agent-based and computational model for Agent_Zero and demonstrates its capacity for generative minimalism. It first explains the replicability of the model before offering an interpretation of the model by imagining a guerilla war like Vietnam, Afghanistan, or Iraq, where events transpire on a 2-D population of contiguous yellow patches. Each patch is occupied by a single stationary indigenous agent, which has two possible states: inactive and active. The discussion then turns to Agent_Zero's affective component and an elementary type of bounded rationality, as well as its social component, with particular emphasis on disposition, action, and pseudocode. Computational parables are then presented, including a parable relating to the slaughter of innocents through dispositional contagion. This part also shows how the model can capture three spatially explicit examples in which affect and probability change on different time scales.

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