Mathematical Model Of Self-regulating Dynamical Systems And Its Applications In Populations Dynamics

In order to study of how and why population size, behavior and structure change intime and space, there has been an increasing interest in the application of systems theory,control theory and information theory to the study of demographic development over thelast decades. This thesis is concerned with the general principles and theories of dynamicalsystems, based on the idea that the rules governing the dynamics of systems are relativelysimple, and that the rich behavior we observe in nature is a consequence of the structure ofthe system rather than of the complexity of the underlying rules. From this perspective,algebraic procedures are developed for evaluating the behavior of self-regulating systemswhose interacting subsystems are systematically linked to behavioral developments, whichare then applied to the analysis of interactions between subgroups of population. Then,dynamic behavior of population system is examined and self-regulating discrete-timeswitching feedback model of the complex system is developed. Based on comparativemethod, the stability, controllability and observability of this model are also examined, andthe results show that the improved model is more reliable and accurate. Finally, this modelis refined and generalized by examining the mechanisms of self-regulating systems andhow demographic systems can maintain their sustainable zero population growth state.