Type-2 fuzzy mathematical modeling and analysis of the dynamical behaviors of complex ecosystems

It is very complex to model, study and analyze the dynamical behavior of the complex ecosystems. Many ecological theoretical problems are based on niche. The niche one species occupies and the relation between niches of different species will directly influence the species’ dynamical behavior. The discussion of niche has been very important to an ecosystem. Fuzzy set theory gave a new creative method to form the niche of a species. Based on broadband effect inherent in membership function of type-2 fuzzy set, the dynamic niche model of fuzzy niche theory is proposed. It is applied to explain the relationship between niches’ separating degree and competition of species and study the dynamical behavior emerging in the competition bio-system. It also analyses the case of the biological synergism in a simulate Lotka–Volterra competition bio-system based on niches.