| Summary: | 碩士 === 國立清華大學 === 物理系 === 105 === Vegetation pattern formation has been successfully described by the non-local
Nagumo model in the past decade. For example, it can be used to explain the
vegetation formation named ”fairy circles” that are observed in vast territories in
southern Angola, Namibia and South Africa. The non-local Nagumo model has
been investigated thoroughly in the past and it exhibits various solutions including
kink/anti-anik, traveling wave and patterns. Since the vegetation of multiple
species is commonly observed in the realistic ecosystems, therefore, we employ the
non-local coupled Nagumo model for multiple species that considers the vegetation
competition between two plant species with different non-local competition
range. We investigate the non-local coupled Nagumo model using a linear stability
analysis and we find the growth patterns changes rapidly as the non-local
range exceeds a critical value. This mode transition phenomenon is investigated
extensively to determine how the mode transition point varies with the coupling
strength. In addition, we discuss how the kernal function affect the mode transition
phenomenon.
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