Bistate Socioecological Processes Exhibiting Complex Nonlinear Behavior-An Analytical Exposition

Generalized nonlinear dynamic models of bistate ecological processes and the feasibility of obtaining closed-form analytical solutions to their governing differential equations represent the topic of this study. The model considered here permits arbitrary nonlinearities within certain very broad limitations, and consequently the study can be of value in modeling and analysis of bistate processes with complex inherent non-linearities in their behavior. The methodology is illustrated by considering as an example a class of these processes wherein the populations of both the species are in the same mode of growth or decay at any given instant. Exact closed-form solutions for the dynamics of a particular process belonging to this class are derived analytically. The resulting responses are discussed to bring out the behavior of the process in all its complexity and thereby demonstrate the value of this technique as an analytical tool in the study of a wide spectrum of nonlinear, bistate, socioecological processes. Also, it is shown that the scope of this study can be enlarged further to cover classes of processes with time-dependent properties as well.