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Yadi Karim - One of the best experts on this subject based on the ideXlab platform.

  • Perturbations Singulières : Approximations, Stabilité Pratique et Applications à des Modèles de Compétition
    2008
    Co-Authors: Yadi Karim, Sari Tewfik
    Abstract:

    Le chapitre 1 rappelle la théorie de Tikhonov pour les systèmes lents-rapides quand la dynamique rapide est stationnaire. Le chapitre 2 examine le théorème de Pontryagin-Rodygin dans lequel la dynamique rapide est périodique. Ce résultat est redémontré en marquant son caractère topologique. Ces résultats concernent les temps finis. Nous indiquons dans le chapitre 3 comment la théorie géométrique des perturbations étudie le cas de la dynamique rapide oscillante. Dans le chapitre 4, des résultats d'approximations pour des temps infinis sont établis quand la dynamique lente converge vers un compact positivement invariant et sont interprétés en termes de stabilité pratique. Le chapitre 5 est consacré au cas où l'équation rapide admet des cycles avec relaxation. Un résultat rigoureux décrit le mouvement lent, la preuve étant basée sur la méthode de stroboscopie. Les résultats sont énoncés dans le cadre des mathématiques classiques mais démontrés à l'aide des outils de l'analyse non standard. Le chapitre 6 est une étude d'un modèle de compétition de dimension 4. Le point de départ se trouve dans des exposés du Pr. C. Lobry qui a constmit un modèle où trois espèces xl, x2 et x3 sont en compétition sur une seule proie s, la coexistence de x2 et x3 semblant possible au travers de simulations numériques, pendant que s et xl oscillent. Nous déterminons le système moyennisé qui décrit l'évolution lente du couple (x2,x3). Nous établissons des conditions suffisantes de persistance et illustrons les résultats par des exemples et des simulations numériques.Chapter 1 recalls Tikhonov's theory for slow-fast systems in case of steady state fast dynamics. Chapter 2 deals with Pontryagin-Rodygin's theorem where the fast dynamics are periodic. We propose a new proof of this theorem emphasizing on its topological features. These results concern bounded lime intervals. We indicate in Chapter 3 how the geometrical theory of perturbations treats the case of the oscillating fast dynamics. In Chapter 4, results for unbounded time intervals are established when the fast dynamics converge to a positively invariant compact subset. These results lead to practical stability theorems. Chapter 5 is devoted to the case where the fast equation has cycles with relaxation. A rigorous result describes the slow motion, the proof being based on the stroboscopic method. The theorems are stated in temms of the classical mathematics and proved with the use on non standard analysis tools. Chapter 6 is a study of a fourth-dimensional competition model. Some talks given by Pr. C. Lobry represent the starting point of this work. C. Lobry built a model of 3 Species xl, x2 and x3 competing on one single Prey Specie s, the coexistence of x2 and x3 seeming possible through some numerical simulations, while s and xl oscillate. We determine the averaged system which describes the slow motion of the couple (x2,x3). We establish sufficient conditions of persistence and we illustrate the results with examples and numerical simulations.MULHOUSE-SCD Sciences (682242102) / SudocSudocFranceF

  • Perturbations singulières : approximations, stabilité pratique et applications à des modèles de compétition
    HAL CCSD, 2008
    Co-Authors: Yadi Karim
    Abstract:

    Chapter 1 recalls Tikhonov's theory for slow-fast systems in case of steady state fast dynamics. Chapter 2 deals with Pontryagin-Rodygin's theorem where the fast dynamics are periodic. We propose a new proof of this theorem emphasizing on its topological features. These results concern bounded time intervals. We indicate in Chapter 3 how the geometrical theory of perturbations treats the case of the oscillating fast dynamics. In Chapter 4, results for unbounded time intervals are established when the fast dynamics converge to a positively invariant compact subset. These results lead to practical stability theorems. Chapter 5 is devoted to the case where the fast equation has cycles with relaxation. A rigorous result describes the slow motion, the proof being based on the stroboscopic method. The theorems are stated in terms of the classical mathematics and proved with the use on non standard analysis tools. Chapter 6 is a study of a fourth-dimensional competition model. Some talks given by Pr. C. Lobry represent the starting point of this work. C. Lobry built a model of 3 Species x1, x2 and x3 competing on one single Prey Specie s, the coexistence of x2 and x3 seeming possible through some numerical simulations, while s and x1 oscillate. We determine the averaged system which describes the slow motion of the couple (x2,x3). We establish sufficient conditions of persistence and we illustrate the results with examples and numerical simulations.Le chapitre 1 rappelle la théorie de Tikhonov pour les systèmes lents-rapides quand la dynamique rapide est stationnaire. Le chapitre 2 examine le théorème de Pontryagin-Rodygin dans lequel la dynamique rapide est périodique. Ce résultat est redémontré en marquant son caractère topologique. Ces résultats concernent les temps finis. Nous indiquons dans le chapitre 3 comment la théorie géométrique des perturbations étudie le cas de la dynamique rapide oscillante. Dans le chapitre 4, des résultats d'approximations pour des temps infinis sont établis quand la dynamique lente converge vers un compact positivement invariant et sont interprétés en termes de stabilité pratique. Le chapitre 5 est consacré au cas où l'équation rapide admet des cycles avec relaxation. Un résultat rigoureux décrit le mouvement lent, la preuve étant basée sur la méthode de stroboscopie. Les résultats sont énoncés dans le cadre des mathématiques classiques mais démontrés à l'aide des outils de l'analyse non standard. Le chapitre 6 est une étude d'un modèle de compétition de dimension 4. Le point de départ se trouve dans des exposés du Pr. C. Lobry qui a construit un modèle où trois espèces x1, x2 et x3 sont en compétition sur une seule proie s, la coexistence de x2 et x3 semblant possible au travers de simulations numériques, pendant que s et x1 oscillent. Nous déterminons le système moyennisé qui décrit l'évolution lente du couple (x2,x3). Nous établissons des conditions suffisantes de persistance et illustrons les résultats par des exemples et des simulations numériques

Sari Tewfik - One of the best experts on this subject based on the ideXlab platform.

  • Perturbations Singulières : Approximations, Stabilité Pratique et Applications à des Modèles de Compétition
    2008
    Co-Authors: Yadi Karim, Sari Tewfik
    Abstract:

    Le chapitre 1 rappelle la théorie de Tikhonov pour les systèmes lents-rapides quand la dynamique rapide est stationnaire. Le chapitre 2 examine le théorème de Pontryagin-Rodygin dans lequel la dynamique rapide est périodique. Ce résultat est redémontré en marquant son caractère topologique. Ces résultats concernent les temps finis. Nous indiquons dans le chapitre 3 comment la théorie géométrique des perturbations étudie le cas de la dynamique rapide oscillante. Dans le chapitre 4, des résultats d'approximations pour des temps infinis sont établis quand la dynamique lente converge vers un compact positivement invariant et sont interprétés en termes de stabilité pratique. Le chapitre 5 est consacré au cas où l'équation rapide admet des cycles avec relaxation. Un résultat rigoureux décrit le mouvement lent, la preuve étant basée sur la méthode de stroboscopie. Les résultats sont énoncés dans le cadre des mathématiques classiques mais démontrés à l'aide des outils de l'analyse non standard. Le chapitre 6 est une étude d'un modèle de compétition de dimension 4. Le point de départ se trouve dans des exposés du Pr. C. Lobry qui a constmit un modèle où trois espèces xl, x2 et x3 sont en compétition sur une seule proie s, la coexistence de x2 et x3 semblant possible au travers de simulations numériques, pendant que s et xl oscillent. Nous déterminons le système moyennisé qui décrit l'évolution lente du couple (x2,x3). Nous établissons des conditions suffisantes de persistance et illustrons les résultats par des exemples et des simulations numériques.Chapter 1 recalls Tikhonov's theory for slow-fast systems in case of steady state fast dynamics. Chapter 2 deals with Pontryagin-Rodygin's theorem where the fast dynamics are periodic. We propose a new proof of this theorem emphasizing on its topological features. These results concern bounded lime intervals. We indicate in Chapter 3 how the geometrical theory of perturbations treats the case of the oscillating fast dynamics. In Chapter 4, results for unbounded time intervals are established when the fast dynamics converge to a positively invariant compact subset. These results lead to practical stability theorems. Chapter 5 is devoted to the case where the fast equation has cycles with relaxation. A rigorous result describes the slow motion, the proof being based on the stroboscopic method. The theorems are stated in temms of the classical mathematics and proved with the use on non standard analysis tools. Chapter 6 is a study of a fourth-dimensional competition model. Some talks given by Pr. C. Lobry represent the starting point of this work. C. Lobry built a model of 3 Species xl, x2 and x3 competing on one single Prey Specie s, the coexistence of x2 and x3 seeming possible through some numerical simulations, while s and xl oscillate. We determine the averaged system which describes the slow motion of the couple (x2,x3). We establish sufficient conditions of persistence and we illustrate the results with examples and numerical simulations.MULHOUSE-SCD Sciences (682242102) / SudocSudocFranceF

Denise Mello Do Prado - One of the best experts on this subject based on the ideXlab platform.

  • Dieta e Relação de Abundância de Panthera Onca e Puma Concolor Com suas Espécies-Presa na Amazônia Central
    Instituto Nacional de Pesquisas da Amazônia, 2010
    Co-Authors: Denise Mello Do Prado
    Abstract:

    A onça-pintada, Panthera onca, e a onça-parda, Puma concolor, ocorrem em simpatria na maior parte das florestas tropicais e sub-tropicais da América e frequentemente têm sido classificadas como predadores oportunistas. No entanto, pouco se sabe sobre a dieta desses predadores na região amazônica e sobre as relações entre a abundância das onças e a abundância de suas espécies-presa. Neste trabalho, nós acessamos a dieta de onça-pintada e de onça-parda por meio de amostras fecais. Estimamos a abundância relativa de espécies-presa diurnas por meio de observação direta em transectos diurnos e de espécies-presa noturnas e das duas espécies de onça por meio de armadilhas de pegadas em quatro áreas com fitiofisonomias distintas na Amazônia Central-Setentrional. A identidade dos predadores foi determinada por meio de análise molecular das amostras fecais, e a identificação das espéciespresa foi feita por meio de identificação dos pêlos presentes nas amostras. A sobreposição da dieta de onça-pintada e onça-parda foi alta em termos da biomassa de diferentes tipos de presas capturadas. A onça-parda capturou mamíferos de pequeno porte (30 kg) contribuíram mais para a biomassa de presas capturadas nos demais locais, que foram analisados de maneira conjunta. Mamíferos arborícolas, principalmente representados pela preguiça-real, ocorreram em alta frequência na dieta de onça-parda na Reserva Ducke e em frequência moderada na dieta de onça-pintada neste local. Os índices de abundância de onça-pintada e onça-parda tenderam a correlacionarse com os índices de abundância de mamíferos terrestres de médio porte (10-30 kg) nas quatro áreas amostradas, mas não com os índices de abundância de mamíferos de pequeno e grande porte. A relação observada com presas de médio porte sugere que os ítens mais importantes na dieta de onça-pintada e onça-parda na região central-setentrional da Amazônia são os mamíferos de médio porte (10-30 kg). Nossos dados de dieta não dão suporte a uma presença significativa de presas de médio porte na dieta das duas onças. Há que considerar, no entanto, que o número de amostras fecais foi pequeno para Viruá, Uatumã e Maracá. Na reserva Ducke, a baixa abundância de espécies-presa de médio porte em função da pressão de caça clandestina pode ser a causa da alta frequência de mamíferos de pequeno porte na dieta dos dois predadores. Uma revisão de estudos de dieta de P. onca e P. concolor em regiões de floresta tropical indicou que em áreas onde não ocorre o veado de cauda branca, Odocoileus virginianus (uma espécie-presa de grande porte), os mamíferos de tamanho médio são os mais frequentes na dieta de ambas as onças. Nas áreas onde O. virginianus ocorre, ele é a presa principal na dieta das duas onças, resultando em uma predominância de mamíferos de grande porte (>30 kg). Possivelmente, as duas onças consomem prioritariamente mamíferos de grande porte onde estes ocorrem em abundância, são fáceis de capturar e não oferecem grandes riscos ao predador, mas em áreas onde este grupo de presas são mais escassos ou perigosos, o grupo de espécie-presa principal passa a ser os mamíferos de médio porte. Quando as presas de grande e médio porte estão menos disponíveis, as onças passam a utilizar os mamíferos de pequeno porte com maior frequência, podendo, inclusive, alimentar-se predominantemente de mamíferos arborícolas, como ocorreu na reserva Ducke. Nossos resultados reforçam as evidências do caráter oportunista do comportamento alimentar de P. onca e P. concolor.Jaguar, Panthera onca, and cougar, Puma concolor, occur sympatrically in most tropical and subtropical evergreen forests on the American continent and have often been classified as opportunistic predators. However, little is known about the feeding ecology of these felids in the Amazon region and about predator-Prey abundance relationships. In this study, we analyzed the diet and Prey availability of jaguar and cougar in 4 localities in northern central Amazonia. Diet was assessed through faecal analysis and Prey availability was estimated by diurnal visual surveys and print traps. Predator relative abundance was estimated by print traps. The identity of the predators was determined by molecular analysis of feaces and the Prey items were identified from hair structure. Overall dietary overlap was high, in terms of mass of different kind of Prey killed. Small-Prey (< 10 kg) was captured more by cougar than medium (10-30 kg) and large Prey (>30 kg) in all localities. Jaguar consumed more small Prey than other groups only in Ducke Reserve, but the large-sized Prey (>30 kg) were the most frequent group in the other localities, which were analyzed together. Arboreal mammals, principally sloths, were found in high frequency in the diet of cougar and moderately in the diet of jaguar at Ducke Reserve. The relative-abundance indexes of jaguar and cougar tended to covary with the abundance indexes of medium-sized (10-30 kg) terrestrial mammals in all localities, but there was no tendency to covary with the abundance indexes of small (30 kg) mammals. The tendency to covary with mediumsized Prey suggests they are the most important food sources for jaguar and cougar in the northern central Amazonian. Our results do not support a significant presence of mediumsized Prey in jaguar and cougar diet. However, we had only a small sample of feces from Viruá, Uatumã and Maracá. In Ducke reserve, the low abundance of medium-sized Prey is likely to be because of poaching. A literature review of jaguar and cougar diets from rainforest regions indicated that, in areas where there are no the white-tailed deer, Odocoileus virginianus (a large Prey Specie), medium-sized Prey are the most frequent Prey in jaguar and cougar diets. In the areas where O. virginianus occurs, it is the main Prey of jaguar and cougar, resulting in a predominance of large Prey (>30 kg) in the diet. Possibly, jaguar and cougar primarily consume large mammals where they occur in abundance, are easy to catch and are not dangerous to predators, but in areas where this group is scarce or dangerous, the main group of Prey is the medium-sized mammals. When easily taken large and medium-Prey are less abundant, jaguar and cougar take more small Prey, as occurred in Ducke reserve. Our results provide further evidence of opportunistic in feeding behavior by jaguars and cougars

Kate Helena Britton - One of the best experts on this subject based on the ideXlab platform.

Kate Helena - One of the best experts on this subject based on the ideXlab platform.