Oscillations in Neuronal Dynamical Systems, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Periodic orbits are one of the basic objects of interest in Dynamical systems. And methods for detecting, counting and determining the periods of periodic orbits are of great interest. In spite of this interest, periodic orbits remain difficult to detect. The most celebrated existence result is the Poincare-Bendixson theorem. Unfortunately, this theorem is false in general for higher dimensional systems. The success of fixed point theory inspired the hope that similar topological techniques could be of use in proving the existence of periodic orbits. In this Thesis we have analyzed some topological and geometrical theories which could be of use in proving the existence of periodic orbits....
Cataloging briefOscillations in Neuronal Dynamical Systems, M.Sc. Thesis Sharif University of Technology ; Razvan, Mohammad Reza (Supervisor)
Abstract
Periodic orbits are one of the basic objects of interest in Dynamical systems. And methods for detecting, counting and determining the periods of periodic orbits are of great interest. In spite of this interest, periodic orbits remain difficult to detect. The most celebrated existence result is the Poincare-Bendixson theorem. Unfortunately, this theorem is false in general for higher dimensional systems. The success of fixed point theory inspired the hope that similar topological techniques could be of use in proving the existence of periodic orbits. In this Thesis we have analyzed some topological and geometrical theories which could be of use in proving the existence of periodic orbits....
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