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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...
Fermentation processes as objects of modelling and high-quality
control are characterized with interdependence and time-varying of process
variables that lead to non-linear models with a very complex structure. This
is why the conventional optimization methods cannot lead to a satisfied
solution. As an alternative, genetic algorithms, like the stochastic global
optimization method, can be applied to overcome these limitations. The
application of genetic algorithms is a precondition for robustness...
Non-linear mixed models defined by stochastic differential equations (SDEs) are considered: the parameters of the diffusion process are random variables and vary among the individuals. A maximum likelihood estimation method based on the Stochastic Approximation EM algorithm, is proposed.
This estimation method uses the Euler-Maruyama approximation of the diffusion, achieved using latent auxiliary data introduced to complete the diffusion process between each pair of measurement instants.
A tuned...
Various particle methods are widely used to model dynamics of complex media. In this work
molecular dynamics and dissipative particles dynamics are applied to model blood flows
composed of plasma and erythrocytes. The properties of the homogeneous particle fluid are
studied. Capillary flows with erythrocytes are investigated.
Recent technological advances including brain imaging (higher resolution in space and
time), miniaturization of integrated circuits (nanotechnologies), and acceleration of
computation speed (Moore’s Law), combined with interpenetration between neuroscience,
mathematics, and physics have led to the development of more biologically plausible
computational models and novel therapeutic strategies. Today, mathematical models of
irreversible medical conditions...
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 study pattern-forming instabilities in reaction-advection-diffusion systems. We
develop an approach based on Lyapunov-Bloch exponents to figure out the impact of a
spatially periodic mixing flow on the stability of a spatially homogeneous state. We deal
with the flows periodic in space that may have arbitrary time dependence. We propose a
discrete in time model, where reaction, advection, and diffusion act as successive
operators, and show that...
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...
We study the coexistence of multiple periodic solutions for an analogue of the
integrate-and-fire neuron model of two-neuron recurrent inhibitory loops with delayed
feedback, which incorporates the firing process and absolute refractory period. Upon
receiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits a
spike with a pattern-related delay, in addition to the synaptic delay. We present a
theoretical framework to view...
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...
Modeling the movement of cells (bacteria, amoeba) is a long standing subject and partial differential equations have been used several times. The most classical and successful system was proposed by Patlak and Keller & Segel and is formed of parabolic or elliptic equations coupled through a drift term. This model exhibits a very deep mathematical structure because smooth solutions exist for small initial norm (in the appropriate space) and blow-up for large norms. This reflects experiments on...
The aim of this paper is to study periodic solutions of Marchuk's model, i.e. the system of ordinary differential equations with time delay describing the immune reactions. The Hopf bifurcation theorem is used to show the existence of a periodic solution for some values of the delay. Periodic dynamics caused by periodic immune reactivity or periodic initial data functions are compared. Autocorrelation functions are used to check the periodicity or quasiperiodicity of behaviour.
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).
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