Abstract
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.