Messaoud Souilah | Searcharxiv

arXiv2024

Identification des paramètres d'un modèle logistique en dynamique des populations avec sortie affine

We study the parameters identification of a dynamic model of a population living in a given host environment governed by a logistic law. We use a statistic Kullback-Leibler type method to derive the algorithm for estimating the parameters of the model in two levels. The first level AIG is an offline algorithm and global it is obtained using the critical points of the reestimation transformation between two parameters. It estimates the parameters in a global iterative manner starting from a block of data. The second level ARE is adaptive recursive and is used online. It constitutes a refinement of the AIG algorithm. The convergence of the AIG algorithm is an open problem. The convergence of the ARE algorithm is demonstrated by constructing a new model, a new space and a new probability law.

math.DS↗

arXiv2024

Global solution and blow-up for the SKT model in Population Dynamics

In this paper, we prove the existence and uniqueness of the global solution to the reaction diffusion system SKT with homogeneous Newmann boundary conditions. We use the lower and upper solution method and its associated monotone iterations where the reaction functions are locally Lipschitz .We study the blowing-up property of the solution, we give a sufficient condition on the reaction parameters of the model to ensure the blow-up of the solution continuous functions spaces.

math.AP↗