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Compartmentalization is a general principle in biological systems which is observable on all size scales, ranging from organelles inside of cells, cells in histology, and up to the level of groups, herds, swarms, meta-populations, and populations. Compartmental models are often used to model such phenomena, but such models can be both highly nonlinear and difficult to work with.Fortunately, there are many significant biological systems that are amenable to linear compartmental models which are often...
Intra-specific competition in population dynamics can be described by integro-differential
equations where the integral term corresponds to nonlocal consumption of resources by individuals
of the same population. Already the single integro-differential equation can show the
emergence of nonhomogeneous in space stationary structures and can be used to model the process
of speciation, in particular, the emergence of biological species during evolution [S. Genieys et al., Math. Model. Nat. Phenom....
We develop a stage-structured model that
describes the dynamics of two competing species each of which have sexual
and clonal reproduction. This is typical of many plants including irises.
We first analyze the dynamical behavior of a single species model. We show
that when the inherent net reproductive number is smaller than one then the
population will go to extinction and if it is larger than one then
an interior equilibrium exists and it is globally asymptotically
stable. Then we analyze...
Complementary analysis of a model of the human immune system after a series of vaccinations, proposed in [7] and studied in [6], is presented. It is shown that all coordinates of every solution have at most two extremal values. The theoretical results are compared with experimental data.
The paper is devoted to the method of computer simulation of protein interactions taking
part in photosynthetic electron transport reactions. Using this method we have studied
kinetic characteristics of protein-protein complex formation for four pairs of proteins
involved in photosynthesis at a variety of ionic strength values. Computer simulations
describe non-monotonic dependences of complex formation rates on the ionic strength as the
result of...
The nonlocal Fisher equation has been proposed as a simple model exhibiting Turing
instability and the interpretation refers to adaptive evolution. By analogy with other formalisms
used in adaptive dynamics, it is expected that concentration phenomena (like convergence to a sum
of Dirac masses) will happen in the limit of small mutations. In the present work we study this
asymptotics by using a change of variables that leads to a constrained Hamilton-Jacobi equation.
We prove the convergence analytically...
We introduce and study conditional differential equations, a kind of random differential equations. We give necessary and sufficient conditions for the existence of a solution of such an equation. We apply our main result to a Malthus type model.
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