Constantinescu, Mara Irina (2025) Uncertainty Quantification and Stability Analysis of the Lotka-Volterra Model Using the Stochastic Galerkin Approach. Bachelor's Thesis, Applied Mathematics.
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Abstract
The classical Lotka-Volterra model describes the population evolution of two interacting species, one a predator, and the other its prey. The paper investigates the model under parametric uncertainty using the Stochastic Galerkin method, where the deterministic system is transformed into a set of coupled ordinary differential equations via generalized Polynomial Chaos Expansion with Legendre polynomials. Analytical and numerical computations are performed for low-dimensional truncation orders to determine the steady states of the system and their stability. Results show that steady states under uncertainty can be stable, unstable, or neither at the same time and additional fixed points emerge with increasing stochastic complexity. A sensitivity analysis further explores the effects of varying model parameters on equilibrium behavior and population evolutions.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Koellermeier, J. and Peypouquet, J.G. |
| Degree programme: | Applied Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 21 Jul 2025 14:22 |
| Last Modified: | 21 Jul 2025 14:22 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/36435 |
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