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 $a_{0}$ (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 $a_{0}$ 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