随机平均法是研究非线性随机动力学*有效且应用*广泛的近似解析方法之一。《Stochastic Averaging Methods and Applications，Volume 2（随机平均法及其应用 下册）》是专门论述随机平均法的著作，介绍了随机平均法的基本原理，给出了多种随机激励（高斯白噪声、高斯和泊松白噪声、分数高斯噪声、色噪声、谐和与宽带噪声等）下多种类型非线性系统（拟哈密顿系统、拟广义哈密顿系统、含遗传效应力系统等）的随机平均法以及在自然科学和技术科学中的若干应用，主要是近30年来浙江大学朱位秋院士团队与美国佛罗里达大西洋大学Y.K.Lin院士和蔡国强教授关于随机平均法的研究成果的系统总结。《Stochastic Averaging Methods and Applications，Volume 2（随机平均法及其应用 下册）》论述深入浅出，同时提供了必要的预备知识与众多算例，以利读者理解与掌握《Stochastic Averaging Methods and Applications，Volume 2（随机平均法及其应用 下册）》内容。
目錄：
Contents1 Stochastic Averaging Methods of Quasi-integrable Hamiltonian Systems Excited by Colored Noises 11.1 Stationary Wideband Noise Excitation 1 1.1.1 SDOF System 21.1.2 MDOF System 131.2 Fractional Gaussian Noise Excitation 281.2.1 Non-internal Resonant Case 301.2.2 Internal Resonant Case 381.3 Combined Harmonic and Stationary Wideband Noise Excitations 471.3.1 Single-DOF System 471.3.2 MDOF System 681.4 Narrowband Randomized Harmonic Noise Excitation 871.4.1 SDOF System 881.4.2 MDOF System 92References 1022 Stochastic Averaging Methods of Quasi-integrable Hamiltonian Systems with Genetic Effective Forces 1052.1 Quasi-integrable Hamiltonian System with Hysteretic Forces 1052.1.1 Equalization of Hysteretic Forces 1052.1.2 Stochastic Averaging for the Equivalent Quasi-Integrable Hamiltonian Systems 1102.2 Quasi-integrable Hamiltonian Systems with Viscoelastic Forces 1232.3 Quasi-integrable Hamiltonian Systems with Fractional Derivative Damping Forces 1392.4 Quasi-integrable Hamiltonian Systems with Time-Delay Forces 160References 1743 Stochastic Averaging Methods of Quasi-generalized Hamiltonian Systems Excited by Gaussian White Noises 1773.1 Quasi-nonintegrable Generalized Hamiltonian Systems 1793.2 Quasi-integrable Generalized Hamiltonian Systems 1903.2.1 Non-internal Resonance 1913.2.2 Internal Resonant Case 1983.3 Quasi-partially Integrable Generalized Hamiltonian Systems 2093.3.1 Non-resonant Case 2103.3.2 Internal Resonant Case 217References 2364 Stochastic Averaging Method of Predator–Prey Ecosystems 2374.1 Classical Lotka-Volterra Predator–Prey Ecosystem 2374.1.1 Deterministic Models 2374.1.2 Stochastic Model 2404.1.3 Stochastic Averaging 2414.1.4 Stationary Probability Density 2434.2 Ecosystem with Predator-Saturation and Predator-Competition 2464.2.1 Deterministic Model 2464.2.2 Stochastic Model 2484.2.3 Stochastic Averaging 2494.3 Ecosystem Under Colored Noise Excitations 2504.3.1 Low-Pass Filtered Stochastic Excitation 2554.3.2 Excitation of Randomized Harmonic Process 2574.4 Time-Delayed Ecosystem 2614.4.1 Deterministic Model 2614.4.2 Stochastic Model 2644.4.3 Stochastic Averaging 2664.5 Ecosystem with Habitat Complexity 2684.5.1 Deterministic Model 2694.5.2 Equilibriums and Stability 2714.5.3 Modified Lotka-Volterra Model 2744.5.4 Stochastic Model and Stochastic Averaging 276References 2825 Several Applications of the Stochastic Averaging Methods in Natural Sciences 2855.1 Motion of Active Brownian Particles 2855.1.1 Deterministic Motion of Active Brownian Particle 2865.1.2 Stochastic Motion of Active Brownian Particle 2895.1.3 Random Swarm Motion of Active Brownian Particles 3045.2 Reaction Rate Theory 3115.2.1 Kramers Reaction Rate Theory 3125.2.2 Reaction Rate Dominated by Energy Diffusion 3155.2.3 Reaction Rate on Multi-dimensional Potential Energy Landscape 3185.2.4 Reaction Rate Under Colored Noise Excitation 3215.2.5 Prediction of Reaction Rate Under Colored Noise Excitation Using the Stochastic Averaging Method in Sect1.1 3245.3 Fermi Resonance 3305.3.1 Pippard Model of Fermi Resonance 3305.3.2 First-Passage Time of Pippard System Under Stochastic Excitation 3325.3.3 Reaction Rate of Fermi Resonance Under Stochastic Excitation 3425.4 Thermal Motion of DNA Molecule 3465.4.1 PBD Model of DNA Molecule 3465.4.2 Stationary Motion of DNA Molecules 3495.5 Conformational Transformation of Biomacromolecule 3555.5.1 Model and Motion of Conformational Transformation 3555.5.2 Stochastic Dynamics of Conformational Transformation 3585.5.3 Denaturation of DNA Molecule 363References 3666 Several Applications of the Stochastic Averaging Methods in Technical Sciences 3716.1 Vortex-Induced Random Vibration 3716.1.1 Hartlen-Currie Wake Oscillator Model 3726.1.2 Hartlen-Currie Model with Fluctuating Wind Excitation—Resonance Case 3736.1.3 Hartlen-Currie Model Under Fluctuating Wind Excitation—Non-resonance Case 3816.1.4 Nonlinear Structural Oscillator 3836.2 Multi-machine Power Systems with Stochastic Excitations 3896.2.1 Model of Single/Multi-machine Power Systems Subjected to Stochastic Excitations 3896.2.2 Stochastic Averaging 3926.2.3 Reliability of Multi-machine Power Systems 3946.3 Ship Rolling Motion 3986.3.1 Rolling Motion Equation of Ship Under Irregular Wave Excitation 3986.3.2 Averaged It？ Stochastic Differential Equation 4006.3.3 Ship Capsize Probability 4046.4 Asymptotic Lyapunov Stability with Probability 1 of Quasi-Hamiltonian Systems 4076.4.1 Asymptotic Lyapunov Stability with Probability 1 of Stochastic Systems 4086.4.2 Maximum Lyapunov Exponent 4106.4.3 Lyapunov Asymptotic Stability with Probability 1 for Quasi-non-i
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