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Jian Wang

From local to global: Complex behavior of spatiotemporal systems with fluctuating delay times

Autor: Jian Wang

ISBN: 978-3-944640-11-2

Seitenzahl: 119

Erscheinungsdatum: 01.03.2014

 

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The aim of this thesis is to investigate the dynamical behaviors of spatially extended systems with fluctuating time delays. In recent years, the study of spatially extended systems and systems with fluctuating delays has experienced a fast growth. In ubiquitous natural and laboratory situations, understanding the action of time-delayed signals is a crucial for understanding the dynamical behavior of these systems. Frequently, the length of the delay is found to change with time. Spatially extended systems are widely studied in many fields, such as chemistry, ecology, and biology. Self-organization, turbulence, and related nonlinear dynamic phenomena in spatially extended systems have developed into one of the most exciting topics in modern science. The first part of this thesis considers the discrete system. Diffusively coupled map lattices with a fluctuating delay are used in the study. The uncoupled local dynamics of the considered system are represented by the delayed logistic map. In particular, the influences of diffusive coupling and fluctuating delay are studied. To observe and understand the influences, the results for the considered system are compared with coupled map lattices without delay and with a constant delay as well as with the uncoupled logistic map with fluctuating delays. Identifying different patterns, determining the existence of traveling wave solutions, and specifying the fully synchronized stable state are the focus of this part of the study. The Lyapunov exponent, the master stability function, spectrum analysis, and the structure factor are used to characterize the different states and the transitions between them. The second part examines the continuous system. The delay is introduced into the reactionterm of the Fisher-KPP equation. The focus of this part of study is the time-delay-induced Turing instability in one-component reaction-diffusion systems. Turing instability has previously only been found in multiple-component reaction-diffusion systems. However, this work demonstrates with the help of the stability exponent that fluctuating delay can result in Turing instability in one-component reaction-diffusion systems as well.
 

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