Author: Hugo Gonzalez VillasantiPublisher:
ISBN:
Category : Dynamics
Languages : en
Pages : 67
Book Description
The first part of this dissertation extends the applicability of stability-preserving mappings to dynamical systems whose evolutionary processes explicitly consider the effect of external perturbations (inputs) and measurements (outputs), via multi-valued operators. We provide definitions for input-to-state stability and input-to-output stability for a general class of systems whose trajectories lie in arbitrary metric spaces, indexed by hybrid time sets. Novel proofs of results such as the ISS-Lyapunov and the small-gain theorem are developed with the use of stability-preserving mappings. The second part, where we employ the theory to model and analyze the complex dynamics found in the interplay of the determinants of mood disorders. The model integrates biopsychosocial findings of the bipolar and depressive spectra, modeling attractors corresponding to mood states such as euthymia, mania, depression, the mixed state, anhedonia, hedonia, and flat or blunted affect, as well as the transitions among these attractors caused by external influences, like stress and medication. Conditions for global stability of euthymia, obtained via a stability analysis, are supported by studies in the neuropsychology literature, while computational analyses provide a novel explanation of the mechanism underlying mood stabilizers.
