A proof of the uniqueness and stability of the equilibriums in the absence of consumer demography; The relationships among mobility, fitness sensitivity and the time for the system to reach equilibrium in the absence of consumer demography; The proof of the relationship between the fitness sensitivity of movement and equilibria in the absence of consumer demography; The proof of the relationships between the fitness-sensitivity of consumers’ movement and regional resource density in the absence of consumer demography

Mathematic proof for the stability of equations without consumer demography and the uniqueness of the solution; This is the numerical simulation to reveal the relationship among mobility, fitness sensitivity and the time to reach equlibrium without considering consumer's demography; Mathematic proof about the relationship between fitness sensitivity and system equlibrium without considering consumer demography; Mathematic proof about the correlation between fitness sensitivity and regional resource density without considering consumer demography