Coupled nonlinear dynamical systems

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.

Name thesis:degree_name

PhD

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics and Astronomy

Year dc:date.available

2000

Author dc:creator

• Sun, Hongyan

Contributors dc:contributor

• Kenneth Showalter
• Larry Halliburton

• Physics

Identifier

https://researchrepository.wvu.edu/etd/1215

OAI identifier oai:identifier

oai:researchrepository.wvu.edu:etd-2218