On orbital stability of synchronous solutions of some singularly perturbed dynamical systems of relaxation-type oscillators with excitatory coupling.

摘要

Singularly perturbed dynamical systems arise naturally in a vast number of different fields from mathematical biology and neuroscience to computer artificial intelligence and pure mathematics. Some of such systems reveal the existence of orbitally stable periodic solutions, often referred to as relaxation cycles, with distinctive fast and slow parts. In this thesis the stability analysis of such solutions of some singularly perturbed dynamical systems is presented. In particular, rigorous proofs of orbital stability of synchronous solutions of some systems of relaxation oscillators with excitatory integral and non-integral coupling terms are given.