Individual-Based Modeling and Nonlinear Analysis for Complex Systems with Application to Theoretical Ecology

One approach to understanding the behaviour of complex systems is individual-based modeling, which provides a bottom-up approach allowing for the consideration of the traits and behaviour of individual organisms. Ecosystem models aim to characterize the major dynamics of ecosystems, in order to synthesize the understanding of such systems and to allow predictions of their behaviour. Moreover, ecosystem simulations have the potential to help scientists address theoretical questions as well as helping with ecological resource management. Because in reality biologists do not have much data regarding variations in ecosystems over long periods of time, using the results of ecological computer simulation for making reasonable predictions can help biologists to better understand the long-term behaviour of ecosystems. Different versions of ecosystem simulations have been developed to investigate several questions in ecology such as how speciation proceeds in the absence of experimenter-defined functions. I have investigated some of these questions relying on complex interactions between the many individuals involved in the system, as well as long-term evolutionary patterns and processes such as speciation and macroevolution. Most scientists now believe that natural phenomena have to be looking as a chaotic system. In the past few years, chaos analysis techniques have gained increasing attention over a variety of applications. I have analyzed results of complex models to see whether chaotic behaviour can emerge, since any attempt to model a realistic system needs to have the capacity to generate patterns as complex as the ones that are observed in real systems. To further understand the complex behaviour of real systems, a new algorithm for long-term prediction of time series behaviour is also proposed based on chaos analysis. We evaluated the performance of our new method with respect to the prediction of the Dow-Jones industrial index time series, epileptic seizure and global temperature anomaly