Qualitative Research Of Sea-air Oscillator Coupling Model For The ENSO

During last twenty years, the frequent global abnormal climate had great impact on social and economic development. As an important part of global climate system, thermal and dynamic characteristics of ocean are essential to long-term evolution of climate,especially annual change. ElNino-Southern Oscillation (ENSO) is the strongest signal in air-sea coupled system, and its importance had attracted increasing attention of the majority of applied mathematics and atmospheric science researchers.Based on this realistic background, in this paper,there are various researches on the ordinary differential equations and functional differen-tial equations of sea-air oscillator coupling model for ENSO.Chapter One, Introduction.The background knowledge of the ElNino phenomenon and research conditions are introduced.Chapter Two, The basic knowledge used in the following research is introduced.Chapter Three, Using the geometric theory of ordinary differential equations, the nature of equilibrium points of autonomous systems, the existence of limit cycles, as well as the equilibrium point at infinity for a class of sea-air oscillator coupling model for ENSO are discussed, and finally the results are shown in the unit disk, forming the global structure of the system.Chapter Four, Using the theory of coincidence degree and the fixed point theorem, a class of delayed sea-air oscillator coupling model with perturbation for ENSO is studied, and the results for the existence and uniqueness of periodic solutions are obtained.