| Dynamics of Active Systems with Nonlinear Excitation of the Phase Contributor(s): Al-Badri, Mayada G. Mohammed (Author) |
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ISBN: 1514833727 ISBN-13: 9781514833728 Publisher: Createspace Independent Publishing Platform OUR PRICE: $45.60 Product Type: Paperback Published: July 2015 |
| Additional Information |
| BISAC Categories: - Mathematics | Numerical Analysis |
| Physical Information: 0.51" H x 6" W x 9" (0.72 lbs) 240 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: In this book, we investigate a version of the phase equation based on a nonlinear self-excitation. We also analyze systems that exhibit self-oscillatory dynamics in order to determine the validity range of the nonlinearly excited phase equation in the parametric space. Specifically, we numerically evaluate the values of the parameters that guarantee the assumptions of slow variations of the phase in space and time and, simultaneously, the key role of the nonlinear self-excitation. We also numerically solve the phase equation with nonlinear self-excitation in two spatial dimensions by finite-difference discretization in space and subsequent numerical integration of a system of ordinary differential equation in time. Irregular dynamics intermitting with periods of slow evolution are revealed and discussed. As a separate task, we derive a forced variant of the phase equation and present selected exact solutions - stationary and oscillatory. Lastly, different forms of the nonlinearly excited phase equation are investigated based on different types of dynamical balance. |