Seeking Sustainability in an Age of Complexity. A New Environmental Paradigm

Using ideas from complexity theory and its application in the areas of ecology, biology, chemistry and medicine this paper shows how the paradigm of complexity is able to offer the conceptual frame in which they can project, evaluate and coordinate processes specific to the living world. Because a lot of environmental models were elaborated in last years, in this article we present some nonlinear techniques which can be used in stability analyses. Mathematical modelling plays a central and increasingly important role in evolution and ecology. This classification aims to help ecologists, biologists and environmentalists navigate the diversity of methods and techniques in mathematical modeling and develop a standardized approach to the application of mathematics in environmental research. Mathematical models have become indispensable tools in contemporary ecology and environmental sciences. We proposed to investigate a model for childhood epidemics such as measles, chickenpox, and mumps to track the dynamics of outbreaks of these contagious diseases. Analyzing the eigenvalues of the liniarized system around each equilibrium point, the locus in the parameters space corresponding to the structural stability of the system is determined.