Predicting system collapse: Two theoretical models

Making precise predictions about the future behavior of a system such as a country's economy, a firm or a lake, or about the population of some species of animal has always been a challenge. While prediction methods and modeling procedures have been developed and used over the past decades, the high degree of uncertainty and complexity that underlie some systems makes it difficult, and in some cases impossible to exactly predict the next states of the system. The purpose of this paper is to present two approaches for identifying potential system Collapse. The first approach is inclination analysis, which examines the state of a system over several windows of time in an effort to predict the final inclination. The second one is based on Support Vector Machines and Kernel methods. Various applications of these approaches as well as their advantages and limitations are also discussed.