Stability analysis of a nonhomogeneous Markovian landscape model

Quantitative methods to analyze spatial patterns of landscapes are an important area of research in landscape ecology. Nonhomogeneous Markov models can be used to represent landscape dynamics; however, methods to analyze the stability of these models are needed. A method for determining the stability is developed in this paper, and its application to a model of vegetation dynamics in southern Texas savanna is also given. Using Lyapunov stability theory, the theorem that the family of these transition matrices will be stable if the symmetric matrices associated with the vertex matrices have matrix measures less than two has been proved. The results of the stability analysis accord well with current understanding of vegetation dynamics in the southern Texas landscape.