https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/9163 2026-06-03T22:52:05Z https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/9344 Title: Intelligent Clustering in Wireless Sensor Networks Authors: HARROUZ, Fatima; Omari, Mohammed / Supervisor; Kaddi, Mohammed / Co-Supervisor Abstract: Wireless Sensor Networks (WSNs) are limited by battery energy, making energy effciency and network lifetime critical challenges. Clustering helps reduce communication overhead and balance energy consumption through effcient Cluster Head (CH) management. This work proposes PUMA-GRID, an energy-effcient protocol that combines the Puma Optimization Algorithm (PUMA) for adaptive CH selection with a lightweight grid based multi-hop routing strategy inspired by k-nearest neighbor (k-NN) logic. During clustering, PUMA selects optimal CHs using a weighted fitness function based on residual energy, distance between nodes and CHs, and distance between CHs and the Base Station (BS), ensuring balanced energy usage and stable cluster formation. For routing, the sensing field is divided into grid cells where neighboring CHs are selected as relays using a k-NN-inspired mechanism to construct shorter and more energy effcient communication paths while reducing long range transmissions and communication overhead. The protocol was evaluated under three BS placement scenarios: central, edge, and external. For each scenario, optimal fitness function weights were first selected before conducting MATLAB simulations with randomly deployed nodes in a 200 × 200 m² sensing field containing up to 600 nodes. PUMA-GRID was then compared with LEACH, Atomic Energy Optimization-based approaches. Simulation results show that PUMA-GRID achieves better network lifetime, residual energy preservation, packet delivery, and communication efficiency, with approximately 35–50% improvement in network lifetime. This improvement is achieved through the combination of adaptive PUMA based CH optimization and effcient kNN inspired routing, which together reduce transmission cost and balance energy consumption across the network. Finally, the framework is mainly designed for static and homogeneous WSN environments, leaving opportunities for future improvements under more realistic conditions. 2026-01-01T00:00:00Z https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/9334 Title: On Some Qualitative Properties of Solutions For Higher Order Neutral Differential Equations Authors: Abdllaoui, Fatima; Rahmane, Mebrouk / supervisor Abstract: This thesis investigates asymptotic, uniform, and exponential stability, as well as boundedness and square integrability of solutions to certain higher-order nonlinear neutral delay differential equations. Serval analytical techniques are employed, chiefly Lyapunov’s second (direct) method, based on constructing candidate Lyapunov functionals. We derive new sufficient conditions that improve and extend many published results. Finally, several illustrative (and numerical) examples are presented to demonstrate the validity of the theoretical findings. These contributions enhance the understanding of neutral delay differential equations and provide a mathematical basis for future studies of more complex systems with multiple delays and/or time-varying coefficients. 2026-01-01T00:00:00Z https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/9302 Title: Contribution to the modeling and mathematical analysis of some stochastic epidemiological models Authors: Kadri, Abdeldjalil; Boudaoui, Ahmed / Supervisor Abstract: Mathematical models, supported by computer simulations, are valuable tools for developing and testing theories related to complex biological systems involving diseases. They facilitate the evaluation of quantitative hypotheses, estimation of key parameters from rael data, sensitivity analysis with respect to parameter changes, and the implementation of optimal control strategies for certain parameters. Modeling is particularly vital in epidemiology, where the underlying complexity of disease transmission is often not fully understood, and conducting experimental studies is generally not feasible. This thesis focuses on the investigation of some nonlinear dynamical systems that describe the spread of infectious diseases. Our main interest lies in the analysis of stochastic epidemic models, especially those based on compartmental frameworks. These models, with or without time delays, incorporate the effects of two specific types of environmental noise: Gaussian white noise and Lévy noise. The objective is to examine how these types of stochastic disturbances influence disease dynamics, thereby contributing to a deeper understanding of epidemic modeling. We were interested in proving the existence of a positive solution, its uniqueness, the extinction of the epidemic, the existence of a stationary distribution, the persistence in mean and illustrate the results by numerical simulation.; Les mod`eles math´ematiques, soutenus par des simulations informatiques, sont des outils pr´ecieux pour d´evelopper et tester des th´eories relatives `a des syst`emes biologiques complexes impliquant des maladies. Ils facilitent l’´evaluation d’hypoth`eses quantitatives, l’estimation des param`etres cl´es `a partir des donn´ees re`el, l’analyse de sensibilit´e par rapport aux variations des param`etres, ainsi que la mise en oeuvre de strat´egies de contrˆole optimal pour certains param`etres. La mod´elisation est particuli`erement essentielle en ´epid´emiologie, o`u la complexit´e sous-jacente de la transmission des maladies est souvent mal comprise, et o`u la r´ealisation d’´etudes exp´erimentales n’est g´en´eralement pas faisable. Cette th`ese porte sur l’´etude de certains syst`emes dynamiques non lin´eaires d´ecrivant la propagation des maladies infectieuses. Notre principal int´erˆet r´eside dans l’analyse des mod`eles ´epid´emiques stochastiques, notamment ceux fond´es sur des cadres compartimentaux. Ces mod`eles, avec ou sans d´elais temporels, int`egrent les effets de deux types sp´ecifiques de bruits environnementaux : le bruit blanc gaussien et le bruit de L´evy. L’objectif est d’examiner comment ces types de perturbations stochastiques influencent la dynamique des maladies, contribuant ainsi `a une compr´ehension plus approfondie de la mod´elisation ´epid´emique. Nous nous sommes int´eress´es `a d´emontrer l’existence d’une solution positive, son unicit´e, l’extinction de l’´epid´emie, l’existence d’une distribution stationnaire, la persistance en moyenne, et `a illustrer les r´esultats par des simulations num´eriques.; تُعد النماذج الرياضية، بدعم من المحاكاة الحاسوبية، أدوات قيّمة لتطوير واختبار النظريات المتعلقة بالأنظمة البيولوجية المعقدة التي تشمل الأمراض. فهي تتيح تقييم الفرضيات الكمية، وتقدير قيم المعلمات الأساسية من المعطيات الواقعية، وتحليل الحساسية لهذة المعلمات ، إضافةً إلى تطبيق استراتيجيات التحكم الأمثل في بعض المعلمات. وتُعتبر النمذجة ضرورية بشكل خاص في علم الأوبئة، حيث غالبا ما تكون آليات انتشار المرض غير مفهومة بالكامل، كما أن إجراء التجارب ليس ممكنا في معظم الحالات. تركز هذه الرسالة على دراسة بعض الأنظمة الديناميكية غير الخطية التي تصف انتشار الأمراض المعدية. وينصب اهتمامنا الرئيسي على تحليل النماذج الوبائية العشوائية، وخصوصا النماذج العشوائية القائمة على تقسيم السكان إلى فئات. تتضمن هذه النماذج، سواء كانت تحتوي على تأخيرات زمنية أو لا، تأثير نوعين محددين من الضوضاء البيئية: الضوضاء البيضاء الغاوسية وضوضاء ليفي. والهدف من ذلك هو دراسة كيفية تأثير هذه الأنواع من العمليات العشوائية على ديناميكيات المرض، مما يساهم في تعميق فهمنا لنمذجة الأوبئة. لقد كنا مهتمين بإثبات وجود حل إيجابي، تفرده، انقراض الوباء، وجود توزيع ثابت، الاستمرار في المتوسط وتوضيح النتائج من خلال المحاكاة العددية. 2025-01-01T00:00:00Z https://dspace.univ-adrar.edu.dz/jspui/handle/123456789/9299 Title: Contributions to the Analysis of a classof Stochastic Differential Equations and Applications Authors: Mouchir, Samiha; Slama, Abdeldjalil / Supervisor Abstract: This thesis investigates a class of stochastic integro-differential equations (SIDEs) with non-instantaneous impulses (INIs) and non-local conditions, focusing on the existence, uniqueness, controllability and stability of the solutions. Key results include the demonstration of existence and controllability for a class of SIDEs governed by fractional Brownian motion, using a generalized Darbo fixed point theory. In addition, the thesis explores a class of fractional order stochastic integral-differential equations (FSIDEs). Existence, uniqueness and stability results using Krasnoselski fixed point theory and the Banach contraction theorem are proven. Numerical methods for the approximation of the solutions are also studied. The numerical methods EM and Θ-EM have been used for the approximation of solutions of the stochastic integro-differential Volterra equations (SVIDEs). The existence, uniqueness and Hölder continuity of the solutions for the SVIDEs, as well as the strong convergence of the Θ-EM method have been studied.// L’objet de cette thèse est l’étude d’une classe d’équations intégro-différentielles stochastiques (EIDSs) avec impulses non instantanées et des conditions non locales, en se concentrant sur l’existence, l’unicité, la contrôlabilité et la stabilité des solutions. Les résultats clés incluent la démonstration de l’existence et de la contrôlabilité pour une classe d’EIDSs gouvernées par un mouvement brownien fractionnaire, en utilisant une théorie généralisée des points fixes de Darbo. De plus, la thèse explore une classe équations intégro-différentielles stochastiques d’ordre fractionnaire (EIDSFs). Des résultats d’existence, d’unicité et de stabilité en utilisant la théorie des points fixes de Krasnoselski et le théorème de contraction de Banach ont été démontrés. Des méthodes numériques pour l’approximation des solutions sont également étudiées. Les méthodes numériques EM et Θ-EM ont été utilisées pour l’approximation de solutions des équations intégro-différentielles stochastiques de Volterra (EIDSVs). L’existence, l’unicité et la continuité de Hölder des solutions pour les EIDSVs, ainsi que la convergence forte de la méthode Θ-EM ont été étudiés. 2025-01-01T00:00:00Z