arXiv subjects
Publications and source records attributed to G. Moza.
A generalized two-dimensional cubic Lotka-Volterra model with infinitesimal parameters is studied. Three different cases have been considered, one non-degenerate and two degenerate. The local behavior of the model has been studied in the three cases. Six bifurcation diagrams with thirty different regions have been obtained in the non-degenerate case, respectively, sixteen diagrams with forty regions in the two degenerate cases.
Degenerate Chenciner bifurcation in generic discrete-time dynamical systems is studied in this work. While the non-degenerate Chenciner bifurcation can be described by 2 bifurcation diagrams, the degeneracy we studied in this work gives rise to 32 different bifurcation diagrams.
Generic results for degenerate Chenciner (generalized Neimark-Sacker) bifurcation are obtained in the present work. The bifurcation arises in two-dimensional discrete-time systems with two independent parameters. We define in this work a new transformation of parameters, which enables the study of the bifurcation when the degeneracy occurs. By the four bifurcation diagrams we obtain, new behaviors hidden by the degeneracy are brought to light.
We study a two-dimensional Kolmogorov system when its two parameters vary in a small neighbourhood of the value $0.$ The local behavior of the system is described in terms of bifurcation diagrams.
Subthreshold oscillations in neurons are those oscillations which do not attain the critical value of the membrane's voltage needed for triggering an action potential (a spike). Their contribution to the forming of action potentials in neurons is a current field of research in biology. The present work approaches this subject using tools from mathematical modeling, more exactly, a neuronal non-smooth map-based model is proposed and studied. The behavior of the model in a noisy medium is also studied.
A two-dimensional Kolmogorov system with two parameters and having a degenerate condition is studied in this work. We obtain local analytical properties of the system when the parameters vary in a sufficiently small neighborhood of the origin. The behavior of the system is described by bifurcation diagrams. Applications of Kolmogorov systems can be found particularly in modeling population dynamics in biology and ecology.