Semester
Fall
Date of Graduation
2000
Document Type
Dissertation
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Physics and Astronomy
Committee Chair
Kenneth Showalter
Committee Co-Chair
Larry Halliburton
Abstract
In this dissertation, we study coupled nonlinear dynamical systems that exhibit new types of complex behavior. We numerically and analytically examine a variety of dynamical models, ranging from systems of ordinary differential equations (ODE) with novel elements of feedback to systems of partial differential equations (PDE) that model chemical pattern formation. Chaos, dynamical uncertainty, synchronization, and spatiotemporal pattern formation constitute the primary topics of the dissertation. Following the introduction in Chapter 1, we study chaos and dynamical uncertainty in Chapter 2 with coupled Lorenz systems and demonstrate the existence of extreme complexity in high-dimensional ODE systems. In Chapter 3, we demonstrate that chaos synchronization can be achieved by mutual and multiplicative coupling of dynamical systems. Chapter 4 and 5 focus on pattern formation in reaction-diffusion systems, and we investigate segregation and integration behavior of populations in competitive and cooperative environments, respectively.
Recommended Citation
Sun, Hongyan, "Coupled nonlinear dynamical systems" (2000). Graduate Theses, Dissertations, and Problem Reports. 1215.
https://researchrepository.wvu.edu/etd/1215