Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 153-160).

Thesis (Ph. D.)--Mathematics, Georgia Institute of Technology, 2005. / Feodor Vainstein, Committee Member ; Dieci Luca, Committee Member ; Yi Yingfei, Committee Member ; Wang Yang, Committee Member ; Shui-Nee, Chow, Committee Chair. Vita. Includes bibliographical references.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 113-114).

We consider a type of forced "Van Der Pol" oscillator where the forced function is periodic and oscillatory around the t-axis. This problem derived from an electrical model. The important issues here is that this circuits presents the spiking phenomena over a one time period and it has important applications in signal processing and digital communication. The three most important problems that we addressed here in this thesis are to compute the number of spikes a solution completes in one time period (it can be used to transform the analog signal into digital information), how the dynamics of the number of spikes change with respect to the parameters amplitude (k) and frequency (w), and when the coupled circuits synchronize (i.e., the driver and the respond are on synchronous). Sophisticated mathematical and numerical analysis has been developed that enable us to give a complete study of the problems above described.