3 research outputs found
Isolation effects in a system of two mutually communicating identical patches
Starting from the Fisher-Kolmogorov-Petrovskii-Piskunov equation (FKPP) we
model the dynamic of a diffusive system with two mutually communicating
identical patches and isolated of the remaining matrix. For this system we find
the minimal size of each fragment in the explicit form and compare with the
explicit results for similar problems found in the literature. From this
comparison emerges an unexpected result that for a same set of the parameters,
the isolated system studied in this work with size L, can be better or worst
than the non isolated systems with the same size L, uniquely depending on the
parameter (internal conditions of the patches). Due to the fact that
this result is unexpected we propose a experimental verification
Crossing-effect in non-isolated and non-symmetric systems of patches
The main result of this article is the determination of the minimal size for
the general case of problems with two identical patches. This solution is
presented in the explicit form, which allows to recuperate all the cases found
in the literature as particular cases, namely, one isolated fragment, one
single fragment communicating with its neighborhood, a system with two
identical fragments isolated from the matrix but mutually communicating and a
system of two identical fragments inserted in a homogeneous matrix. It is also
addressed the new problem of a single fragment communicating with the matrix,
with different life difficulty of each side. As application, it is found that
the internal condition can set which system is the worst to life. This
prediction confirms and extends the prediction already found in the literature
between isolated and non-isolated systems
Habitat fragmentation: the possibility of a patch disrupting its neighbor
This paper starts from the Fisher-Kolmogorov-Petrovskii-Piskunov equation to
model diffusive populations. The main result, according to this model, is that
two connected patches in a system do not always contribute to each other.
Specifically, inserting a large fragment next to a small one is always positive
for life inside the small patch, while inserting a very small patch next to a
large one can be negative for life inside the large fragment. This result,
obtained to homogeneously fragmented regions, is possible from the general case
expression for the minimum sizes in a system of two patches. This expression by
itself is an interesting result, because it allows the study of other
characteristics not included in the present work