Modeling of stochastic equations, Applications in physics and biology

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dc.contributor.authorKHELOUFI Yasmina
dc.date.accessioned2022-10-27T08:05:16Z
dc.date.available2022-10-27T08:05:16Z
dc.date.issued2021-11-30
dc.description.abstractIn this thesis, we study the persistence of properties of a given classical deterministic differential equation under a stochastic perturbation of two distinct forms: external and internal. The first case corresponds to add a noise term to a given equation using the framework of Itô or Stratonovich stochastic differential equations. The second case corresponds to consider parameter dependent differential equations and to add a stochastic dynamics on the parameters using the framework of random ordinary differential equations. Our main concerns for the preservation of properties are stability/instability of equilibrium points and simplictic /Poisson Hamiltonian structures. We formulate persistence theorem in these two cases and prove that the cases of external and internal stochastic perturbations are drastically different. We then apply our results to develop a stochastic version of the Landau-Lifshitz equation. We propose an invariantization method for perturbations in the Itô case which can be used to restore invariance. We then apply our results to develop a stochastic version of the Landau-Lifshitz equation. Finally, we select the stochastic models to Hodgkin-Huxley Reaction-Diffusion preserving viability. Then, we project these results on a Networks represented by a graph of N neurons, adding an excitatory nonlinear coupling between neurons.
dc.formatpdf
dc.identifier.urihttps://dspace.univ-oran1.dz/handle/123456789/232
dc.language.isofr
dc.publisherUniversité oran1 Ahmed Ben Bella
dc.subjectStochastic differential equations
dc.subjectmodel validation
dc.subjectLandau-Lifshitz Equation
dc.subjectItô equations
dc.subjectStratonovich equations
dc.subjectequilibrium points
dc.subjectferromagnetism
dc.subjectPoisson Hamiltonian
dc.subjectHodgkin-Huxley
dc.subjectN neurons
dc.titleModeling of stochastic equations, Applications in physics and biology
dc.typeThesis
grade.Co-rapporteurBelaib Lekhmissi, Professeur, Université Oran 1
grade.ExaminateurTelmcani Mounir, MCB, Université de science et technologie, Oran
grade.ExaminateurOuahab Abdelkrim, Professeur, Université de Djilali Liabes, SBA
grade.ExaminateurAiboudi Mohammed, Professeur, Université Oran 1
grade.InviteBenfriha Habib, Professeur, Université Oran 1
grade.PrésidentNachi Khadra, Professeur, Université Oran 1
grade.RapporteurCresson Jacky, Professeur, Université de Pau et des pays de l’Adour, France
l'article.1.RevueProceedings of Institute of Mathematics and Mechanics
l'article.1.RéférenceProceedings of Institute of Mathematics and Mechanics. No.1, 75-89
l'article.1.TitreA stochastic invariantization méthode for Itô stochastic perturbation of différentiel équations
l'article.2.DateParution(2019)
l'article.2.RevueJournal of Mathematical physics
l'article.2.Référence60, 083512 (2019)
l'article.2.TitreSélection of a stochastic Landau-Lifshitz equation and the stochastic persistance Problem
la.MentionTrès honorables
la.SpécialitéMathématiques appliquées
la.coteTH5279
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Thèses de Doctorat "Mathématique"