Researches Interests
Dynamical Systems (stability, bifurcations and analysis of complex behaviors) and their applications to the modeling of the evolution of Economic, Financial, Social, Biological and Physical systems. The main results have been obtained in the anlysis of noninvertible maps of the plane, following the pioneering works of I. Gumowski and C. Mira. These tools have been improved and applied in the study of the dynamics in smooth models, piecewise-smooth and discontinuous ones.
Recent research fields include:
- Global properties and bifurcations of attracting sets and basins of attraction in discrete time dynamical systems: homoclinic bifurcations and contact bifurcations that change the topological structure of attractors or basins of attraction.
- Dynamic properties of discrete dynamical systems and global bifurcations in iterated two-dimensional maps not defined in the whole plane due to the presence of a vanishing denominators, and related properties of focal points, prefocal curves, lobes, crescents, unbounded sets of attraction.
- Global qualitative analysis of discrete dynamical systems represented by the iteration of noninvertible maps, and study of their properties and global bifurcations by the use of critical sets. Problems of ultimate boundedness and delimitation of basins' boundaries. Applications to the description of long-run complex dynamics and problems of equilibrium selection in dynamic models for Economics, Finance and Social Sciences.
- Symmetric dynamical systems and related problems of chaos synchronization, on-off intermittency, riddling and blowout bifurcations related to the presence of Milnor attractors. Applications to dynamic symmetric games.
- Chaotic maps having an analytical solution.
- Border collision bifurcations in piecewise smooth maps, continuous and discontinuous.
- Dynamic modeling in Economic, Finance and Social Sciences: dynamic oligopoly games, models of economies with boundedly rational agents (and related problems of expectations and learning schemes) models of economies with heterogeneous agents, nonlinear models of business cycle.