Intro -- Preface -- Contents -- Abbreviations -- Symbols -- 1 Introduction -- 2 Preliminaries -- 2.1 Limit Cycle and Semi-stable Limit Cycle -- 2.2 Criterion of Semi-stable Limit Cycle -- 2.2.1 Limit Cycles of Oscillatory Approach and Monotone Approach -- 2.2.2 Criterions -- 2.3 Feature Scale, Scale-Free Domain, Fractal, Random Fractal, Dimension -- 2.4 Iterative Function System and Fractal -- 2.5 Dissipative System -- 2.6 Attractor, Attracting Set, Basin of Attraction, Strange Attractor, and Semi-strange Attractor -- 2.7 Relationship between Semi-stable Limit Cycles and Semi-strange Attractors -- 2.8 Elementary Reaction and Reaction Rate -- 2.9 Lagrangian Particle Dynamic System -- 3 Universal Mathematical Model of Mesoscale Eddy -- 3.1 Mesoscale Eddy -- 3.2 Mathematical Model of Mesoscale Eddy -- 3.2.1 Bounded Motion -- 3.2.2 Movement Asymptotic Unity and Uniform Tendency -- 3.3 Universal Mathematical Model of Mesoscale Eddy -- 3.3.1 Momentum of a Stochastic Ellipse -- 3.3.2 Elementary Reaction Rate -- 3.3.3 Basic Mathematical Model of Mesoscale Eddy -- 3.3.4 Universal Mathematical Model of Mesoscale Eddy -- 4 Semi-stable Limit Cycle in Mathematical Model of Mesoscale Eddy -- 4.1 Analysis of Parameter Distribution of Stable and Unstable Limit Cycles -- 4.1.1 α and β are Positive and m is Odd -- 4.1.2 α and β are Negative and m is Odd -- 4.1.3 α is Positive, β is Negative and m is Odd -- 4.1.4 α is Negative, β is Positive and m is Odd -- 4.1.5 m is a Decimal -- 4.2 Stable Limit Cycle -- 4.3 Unstable Limit Cycle -- 4.4 |