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Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a single set of parameters. The procedures of population parametrization (for instance using SAEM algorithms) are then very long and in some cases...
We study a reaction-diffusion equation
with an integral term describing nonlocal consumption of resources
in population dynamics. We show that a homogeneous equilibrium can
lose its stability resulting in appearance of stationary spatial
structures. They can be related to the emergence of biological
species due to the intra-specific competition and random
mutations.
Various types of travelling waves are observed.
We present a three species model describing the degradation of substrate by
two competing populations of microorganisms in a marine sediment. Considering diffusion
to be the main transport process, we obtain a reaction diffusion system (RDS) which we
study in terms of spontaneous pattern formation. We find that the conditions for patterns
to evolve are likely to be fulfilled in the sediment. Additionally, we present simulations
that are consistent with experimental data from the literature. We...
Parameterization of zooplankton functional response is crucial for constructing plankton models. Theoretical
studies predict enhancing of system stability in case the response is of sigmoid type. Experiments on feeding in laboratories tell us in
favor of non-sigmoid types for most herbivorous zooplankton species. However, recent field observations show that the overall functional
response of zooplankton in the whole euphotic zone can exhibit a sigmoid behavior even when the response for the same...
In this paper, we are concerned with a delayed multispecies competition predator-prey dynamic system with Beddington-DeAngelis functional response. Some sufficient conditions which guarantee the existence of a positive periodic solution for the system are obtained by applying the Mawhin coincidence theory. The interesting thing is that the result is related to the delays, which is different from the corresponding ones known from literature (the results are delay-independent).
Existence and stability of periodic solutions are studied for a system of delay
differential equations with two delays, with periodic coefficients. It models the
evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous
leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding
function leads to the proof of the existence of a strictly positive periodic solution by a
theorem of Krasnoselskii....
Some new techniques for finding periodic travelling waves are discussed.
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