2- رياضيات

Permanent URI for this collectionhttp://172.16.2.43:4000/handle/123456789/579

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2021Sur quelques équations d'évolution de type hyperbolique avec retard
(Université Larbi Tébessi Tébessa, 2021) DRID, Faouzi; DJEDDI, Nassim
Le but de ce travail (étudié par M. Remil et H. Ali[8]) est d’étudier la décroissance d’énergie de l’équation d'Onde viscoélastique sous certaines conditions relatives aux termes de retard variables et à la fonction de relaxation g. Pour étudier l'existence globale de la solution, nous avons utilisé la méthode d'approximation de Galerkin.
About stability analysis in epidemic reaction-diffusion model
(Larbi Tebessi University - Tebessa, 2022) Rahma, Rechache; Racha, Guemmadi
The purpose of this thesis is to study the local and global asymptotic stability of the nonnegative constant steady states of an epidemic reaction-diffusion system (susceptible-infectious) with a nonlinear incidence in the case of ordinary and partial differential equations depending on the basic reproduction number, with determining the linearity of the studied system in both cases . Where the local asymptotic stability is determined by the nature of the eigenvalues, but for the global asymptotic stability we use the Lyapunov method, in addition to illustrate the analytical results through numerical examples
About Stable and Unstable Sets
(Larbi Tbessi University – Tebessa, 2020) Gouasmia, Souhaila; Ghazli, Imane
First of all, a simplified study of stable and unstable sets is presented, with special mention of manifolds. In the first chapter, we dealt with definitions and basic characteristics and the most important thing it was the classification of the manifolds, where we classified them into three types: the stable manifold, the unstable manifold, and the central manifold. In the second chapter, we examined the phenomenon of chaos through the boost converter in equations of a certain shape. We carefully analyzed complex behavior in several parameters and then finally arrived at the case in which robust chaos occurs. In the third chapter, we attached great importance to stability theories with Lyapunov’s concept, and then expanded to the LaSalle’s principle. We also passed instability theories. We point out that we have annotated most of the definitions and theories with several examples that enabled us to identify the importance of these theories in our practical life.
About the dynamics of Zeraoulia-Sprott mapping
(Larbi Tébessi University Tébessa, 2021) Bouthaina, Guenez; Khouloud, Redjeb
The objective of this thesis is to study the dynamical behaviors of the Zeraoulia- Sprott mapping. In particular, this map is the first simple rational map whose fraction has no vanishing denominator and gives chaotic attractors .  In the first chapter, we mentioned some important and comprehensive concepts of dynamical system theory.  In the second chapter, we introduced a two-dimentional smooth discrete bounded map capable of generating multi-fold strange attractors .  In the third chapter we studied periodic 2-orbits of the Zeraoulia-Sprott mapping and we investigete also the bounded and unbounded orbits. Resumé
Aboutt Ensemblle Conttrollllabiilliitty Off Parametter Dependentt Systtems
(Larbi Tebessi University - Tebessa, 2022) Brahmi, Belqys; Belgacemi, Loubna
This memory provides an overview of recent developments in ensemble controllability.Inparameter- dependent linear systems,we look at various ensemble control concepts that have been actively developed over the past decade As an example ,we cite the work of Li [9] and Khaneja [10]. The goal of the control function is to steer the ensemble system to a desired parameter independent state,by implementing parameter-independent open loop controls, then necessary and sufficient conditions for ensemble control are established using methods from complex approximation theory. We consider the problem of ensemble controllability for finite and infinite linear systems, and we provide an overview of the observational ensemble due to its strong connection with the memory theme.
Accélération de la convergence globale de la méthode du gradient
(Universite laarbi tebessi tebessa, 2019) Keddache, Kaouther; Ait djoudi, Wafa
Dans ce travail on va définir des algorithmes d'accélérations de la convergence de la méthode du gradient. On étudiera la convergence globale de ces algorithmes, en utilisant la recherche linéaire inexacte de Wolfe ([34],[35]) et d'Armjo ([4]). Dans [18] et [33], Benzine, Djeghaba et Rahali ont étudié ce problème en utilisant une recherche linaire exacte et une recherche linaire inexacte d'Armijo, et dans [14], Benzine et Degaichia ont étudié le même problème en utilisant une recherche linéaire inexacte de Wolfe. Le but de ce travail c'est accélérer de la convergence de la méthode du gradient et comparer entre ces algorithmes
Acceleration of the convergence of the gradient method by using the conjugate gradient
(University Larbi Tébessi – Tébessa, 2024-06-09) BAHI, Amina
The conjugate gradient method is considered one of the most important methods used to speed up the gradient algorithm, for this purpose, several related algorithms have been developed. We will present a new method that accelerates the convergence of the gradient method (the higher slope method) using a new version of the conjugate gradient and a powerful non-exact linear Wolf search. It will be shown that this algorithm generates descent trends and converges globally.
Adaptive Control for Fractional-Integer Order Systems Synchronization
(Echahid chikh Larbi Tébessi University-Tébessa, 2024-06-08) AOUICHAT, Djihane
In this work, we used an adaptive control method to achieve synchronization between fractional and integer order chaotic systems based on Lyapunov stability theory with unknown system parameters. We verified the results using numerical simulations through the use of MATLAB.
Analyse dynamique d’un nouveau type de synchronisation chaotique discrète
(Universite laarbi tebessi tebessa, 2017) BOUDIAR, Houria; BOUAKKAZ, Maroua
Ce mémoire a pour objet l'étude de synchronisation des systèmes chaotiques discrets. Basé sur la théorie de stabilité des systèmes linéaires et la théorie de Lyapunov, des nouveaux schémas de synchronisation entre des systèmes chaotiques discrets avec des dimensions différentes, sont dérivés. Les simulations numériques sont utilisées pour valider les résultats proposés
Analyse et dynamiques de quelques 3D systèmes chaotiques
(Universite laarbi tebessi tebessa, 2019) kAMEL, Zina; BOUALI, Amel
Dans ce travail, nous nous intéressons à l’étude des phrases dynamiques chaotiques tridimensionnelles en les analysant et en mettant en évidence certaines caractéristiques importantes telles que la recherche de points fixes et de points de stabilité. Et pour prouver l'anarchisme de ces phrases dynamiques pour certaines valeurs des modes de complexité, en trouvant des valeurs pour le Lyapunov de la phrase, D'autre part, l'analyse dynamique de ces phrases était basée sur les diagrammes et les valeurs de Lyapunov, ou sur la valeur maximale des valeurs de Lyapunov pour la phrase dynamique, ainsi que sur les schémas en cascade correspondant aux valeurs de média de cette phrase. Et ensuite, vérifiez les résultats en utilisant une simulation numérique via Matlab.
An analytic study of an epidemiological model as system of non-linear equations
(Université Echahid Chikh Larbi Tébessi -Tébessa, 2023-06-04) MELLAH, Salsabil
The objective of this thesis is to introduce the field of epidemiology and its relationship with mathematics, as well as how it is modeled using partial differential equations. We specifically focus on the epidemic reaction-diffusion model for the spread of HIV, with the aim of studying the long-term stability of its solutions. We demonstrate that the model contains two types of equilibrium points for solving the proposed system, which describes the transmission of the infectious disease among individuals. The epidemic model is analyzed using the reproductive number, R0. We study both local and global stability using the Jacobian matrix and the appropriate Lyapunov function. Finally, we present numerical examples of simulation processes that illustrate the findings discussed throughout the thesis.
Analytical and Numerical Analysis of A Generalized Non Standard Volterra Integro-Differential Equations
(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) KHALED, Soumia
• Fredholm and Volterra integral equations hold a significant position in mathe- matics due to their wide-ranging applications across various scientific fields. • In this thesis, we focus on a specific form of the non linear, non standard, integro-differential Volterra equation. • Using Schauder fixed point theorem, we establish the existence and unique- ness for the solution of this integro-differential Volterra equation under well-defined conditions. • We then apply the Fibonacci Wavelet Collocation method to obtain an approximate solution to this integro-differential equation, followed by illustrative examples demonstrating the obtained results.
Asymptotic stability and explosion of solutions for a class of hyperbolic problem with delay time.
(University of Echahid Cheikh Larbi Tébessi -Tébessa, 2025-06-02) SLIMANI, Ouidad
In this work, we investigated the stability of solutions using the energy method, and finite time blow-up of solutions through a direct approach based on Lyapunov functionals, for certain classes of nonlinear evolution equations. First, the theoretical concepts and methodological tools introduced in this study provide a foundational framework for the detailed results and analyses presented in the subsequent chapters. Next, we established the asymptotic stability of the solution to a Kirchhoff type viscoelastic wave equation that includes Balakrishnan Taylor damping and a time delay term. By constructing an appropriate Lyapunov functional, employing differential inequalities, we proved that the total energy of the system decays to zero over time, despite the additional complexity introduced by the memory and delay effects. Finally, we examined the finite time blow up of solutions for a problem involving a time delay term. Our objective was to determine sufficient conditions under which the solution either decays to zero as time approaches infinity or blows up in finite time, depending on the interplay between the source and damping terms in the evolution equation. From our literature review, we observed that classical models often incorporate nonlinear damping and first order perturbation terms, both of which have been extensively studied.
Autour les opérateurs de dérivation généralisée
(Universite laarbi tebessi tebessa, 2019) Latreche, Bouthaina; Achi, Rahma
Une synthèse bibliographique concernant les théorèmes et les définitions que nous allons utiliser dans les autre chapitres fait l’objet du premier chapitre. Au second chapitre on a donné la forme de Jordan pour l’opérateur de dérivation généralisée ()= {On a obtenu une condition suffisante pour que  a la forme de Jordan Au troisième chapitre, on étudie l’image numérique d’un opérateur linéaire borné et on donne quelques propriétés de l’image numérique d’une dérivation. Au dernier chapitre on a initie l’étude sur l’orthogonalité de l’image au noyau de la dérivation et l’étude des opérateurs fini
Bifurcation in economic grawth model to transformed ode
(Larbi Tebessi University - Tebessa, 2022) Abdallah, HABHOUB; Laila, GATTAL
Our workfocusesonstudyingtwopapersdeeply,wherewescrutinizeanddis- cuss themainpaperofGuerrinietal.[?], whichisconsideredageneralization of KrawiecandSzydlowskiwork[?]. Whither,theauthorsinvestigatedthedy- namics ofthemodi_edKaldormodelandconcludedgivingthemtheresultthat the limitcyclebehaviorisindependentoftheassumptionthattheinvestment function iss-shaped.Inthisstudy,asanassumption,supposedthelinearfunc- tion I(Y ), andonlythetime-delayparameterplayacrucialroleincreatingthe limit cycle.Also,theyshowedthatforasmalltime-delayparameter,inthelin- ear approximation,theKaldor_KaleckimodelassumestheformoftheLiénard equation. Alinearstabilityanalysisincludingthetimedelayisshowntobean accurate predictorofthecritical T for the_rstbifurcation.As T is increased, the systembifurcatestothelimitcyclebehavior,thentomultipleperiodicand aperiodiccyclesoreventuallytendstowardsthechaoticbehaviorviatheperiod doubling cascaderoutetotheturbulence. Guerrini etalstudiedapossiblebifurcationexpectedtoachangeofthepa- rameter valuesoftheKaldor-Kaleckigrowthmodel,which,theyconsidertwo simplest casesofthreeandfour-dimensionaldynamicalsystems,thatwereob- tained throughthelinearchaintrickfromtheKaldor-Kaleckigrowthmodel with distributeddelay.Forbothmodels,theexistenceconditions'oftheHopf bifurcation withrespecttothetimedelayparameterandtherateofgrowthpa- rameter areestablished.Finally,wediscussthenumericalstudyintheprevious papers
Bifurcation de cycles limites dans un centre à quatre dimensions et à deux dimensions isochrones cylindre
(Universite laarbi tebessi tebessa, 2017) DEBBACHE, Khaoula; BOUAKAZ, Khaoula
Dans ce mÈmoire, on utilise la mÈthode de moyennisation du premier ordre pour Ètudier les cycles limites du systËme di§Èrentiel perturbÈ sous la forme x_ = Ax + "F (x): o˘ A = 0 BB@ 0 1 0 0 1 0 0 0 0 0 0 n 0 0 n 0 1 CCA et " est un paramËtre su¢ samment petit, F : R 4 ! R 4 est un polynÙme de la forme F (x) = F1 (x) + FN (x) avec FK un polynÙme homogËne de degrÈ k en les variables x = (x1; x2; x3; x4). Nous Ètudions aussi líexistence des cycles limites du systËme di§Èrentiel perturbÈ suivant 8 >>< >>: x_ = x (x 2 + y 2 1) y + "P (x; y; z) y_ = y (x 2 + y 2 1) + x + "Q (x; y; z) z_ = x p x 2 + y 2 + "R (x; y; z). O˘ " est un paramËtre su¢ samment petit et P; Q et R sont des polynÙmes arbitraires en les variables (x; y
Bifurcation des cycles limites via la théorie de moyennisation
(Universite laarbi tebessi tebessa, 2019) Harkat, Khelil; Aimene, Imad
Dans ce mémoire, nous étudions premièrement l'existence de cycles limites du système différentiel à quatre dimensions ( ), 0 x   A x F x où  est un paramètre suffisamment petit, , 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0                 A  et 4 4 F :R R est donné par F(x) Ax (k x)b, T   avec (R) AM4 , , R \{0} 4 k b et  :R  R la fonction linéaire par morceaux            , si [1, ), R . 0, si ( ,1), ( ) mx x m x  x La seconde partie de ce travail est l'étude de l'existence de cycles limites d'un satellite rigide dumbbell dans un orbite circulaire ayant des équations de mouvement de la forme                                                  1 3cos sin cos , , , , , 2 1 tan 3sin cos , , , , , 2 2 2 2 2 1 2 2 dt d dt d F t dt d dt d dt d dt d F t dt d dt d dt d                      où  est un paramètre suffisamment petit et   1 2 F , F sont des fonctions lisses périodiques en t.
Bifurcations of someZeraoulia-Sprottmappings
(Larbi Tebessi University - Tebessa, 2022) Zedira, ZINEB; Khaled, Assia
The aim of this memory is to study the dynamical behaviors of some Zeraoulia-Sprott piecewise smooth mappings in one and two dimensional. These maps are characterized by a highly dispersed behavioral nature that reaches the extreme of robust chaos as a result of the border collision bifurcations that occurs especially in this type of maps
The blow-up and global existence of solutions of cauchy problems for a time fractional diffusion equation
(Larbi Tbessi University – Tebessa, 2017) Boussahela, S; Mouaia, F.
Blow-up Phenomena for some nonlinear pseudo-parabolic equation
(Université Echahid Chikh Larbi Tébessi -Tébessa, 2024-06-09) BARHOUM, Aya
The main objective of this thesis is an analytical study of the blow-up of solutions for certain pseudo-parabolic equations. In the first study, we focused on equations with source and damping terms with fixed exponents. To prove the blow-up, we used the method of differential inequalities. In the second study, we highlighted pseudo-parabolic equations with variable exponents. By also using differential inequalities, we obtained the blow-up of the solution. Finally, we study the blow-up of solutions for pseudo-parabolic equations with variable exponents in the presence of a matrix with variable coefficients.

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