{"id":{"repo_id":"wvu","oai_identifier":"oai:researchrepository.wvu.edu:etd-2218"},"canonical_url":"https://search.dev.ndltd.org/etd/wvu/oai:researchrepository.wvu.edu:etd-2218","repository":{"repo_id":"wvu","name":"West Virginia University","base_url":"https://researchrepository.wvu.edu/do/oai/"},"display":{"title":"Coupled nonlinear dynamical systems","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Sun, Hongyan"],"institution":null,"degree_name":"PhD","degree_level":"Dissertation","degree_discipline":"Physics and Astronomy","degree_department":null,"school":null,"contributors":["Kenneth Showalter","Larry Halliburton"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2000,"date_issued":"2000-12-01T08:00:00Z","date_published":"2000-12-01T08:00:00Z","updated_at":"2026-07-24T06:15:23Z","subjects":["Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://researchrepository.wvu.edu/etd/1215"],"render_values":[{"text":"https://researchrepository.wvu.edu/etd/1215","href":"https://researchrepository.wvu.edu/etd/1215","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.33915/etd.1215","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kenneth Showalter","Larry Halliburton"]},{"key":"dc:creator","label":"Author","values":["Sun, Hongyan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-01-17T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics and Astronomy"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.33915/etd.1215","https://researchrepository.wvu.edu/etd/1215"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Coupled nonlinear dynamical systems"]}]}],"canonical_facts":{"dc:contributor":["Kenneth Showalter","Larry Halliburton"],"dc:creator":["Sun, Hongyan"],"dc:date.available":["2019-01-17T08:00:00Z"],"dc:description.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."],"dc:identifier":["https://doi.org/10.33915/etd.1215","https://researchrepository.wvu.edu/etd/1215"],"dc:subject":["Physics"],"dc:title":["Coupled nonlinear dynamical systems"],"thesis:degree_discipline":["Physics and Astronomy"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["PhD"]},"updated_at":"2026-07-24T06:15:23Z"}