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Null controllability of a coupled model in population dynamics

Younes Echarroudi (2023)

Mathematica Bohemica

We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed...

Nutrient-phytoplankton-zooplankton interaction with variable yields

Joydeb Bhattacharyya, Samares Pal (2013)

Applicationes Mathematicae

A three dimensional predator-prey-resource model is proposed and analyzed to study the dynamics of the system with resource-dependent yields of the organisms. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in the absence of predation. Local stability of the system is obtained in the absence of one or more of the predators and in the presence of all the predators. Under appropriate...

On bilinear kinetic equations. Between micro and macro descriptions of biological populations

Mirosław Lachowicz (2003)

Banach Center Publications

In this paper a general class of Boltzmann-like bilinear integro-differential systems of equations (GKM, Generalized Kinetic Models) is considered. It is shown that their solutions can be approximated by the solutions of appropriate systems describing the dynamics of individuals undergoing stochastic interactions (at the "microscopic level"). The rate of approximation can be controlled. On the other hand the GKM result in various models known in biomathematics (at the "macroscopic level") including...

On monotone and Schwarz alternating methods for nonlinear elliptic PDEs

Shiu-Hong Lui (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...

On Monotone and Schwarz Alternating Methods for Nonlinear Elliptic PDEs

Shiu-Hong Lui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The Schwarz alternating method can be used to solve elliptic boundary value problems on domains which consist of two or more overlapping subdomains. The solution is approximated by an infinite sequence of functions which results from solving a sequence of elliptic boundary value problems in each of the subdomains. In this paper, proofs of convergence of some Schwarz alternating methods for nonlinear elliptic problems which are known to have solutions by the monotone method (also known as the method...

On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay

S. Ruan (2009)

Mathematical Modelling of Natural Phenomena

In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey models, generalized Gause-type predator-prey models with harvesting, etc. Bogdanov-Takens bifurcations...

Currently displaying 261 – 280 of 449