分歧理论和突变理论-动力系统-V
分歧理论和突变理论-动力系统-V作者:阿诺德 开 本:其它 书号ISBN:9787030234933 定价:128.0 出版时间:2009-01-01 出版社:科学出版社 |
7.6. The Degenerate Family and Its Neighborhood iFunctioSpace
7.7. Birth of Tori ia Three-Dimensional Phase Space
8. Attractors and their Bifurcations
8.1. The Likely Limit Set According to Milnor (1985)
8.2. Statistical Limit Sets
8.3. Internal Bifurcations and Crises of Attractors
8.4. Internal Bifurcations and Crises of Equilibria and Cycles
8.5. Bifurcations of the Two-Dimensional Torus
Chapter 4. RelaxatioOscillations
1. Fundamental Concepts
1.1. AExample: vader Pors Equation
1.2. Fast and Slow Motions
1.3. The Slow Surface and Slow Equations
1.4. The Slow Motioas aApproximatioto the Perturbed Motion
1.5. The Phenomenoof Jumping
2. Singularities of the Fast and Slow Motions
2.1. Singularities of Fast Motions at Jump Points of Systems with One Fast Variable
2.2. Singularities of Projections of the Slow Surface
2.3. The Slow Motiofor Systems with One Slow Variable
2.4. The Slow Motiofor Systems with Two Slow Variables
2.5. Normal Forms of Phase Curves of the Slow Motion
2.6. Connectiowith the Theory of Implicit Differential Equations
2.7. Degeneratioof the Contact Structure
3. The Asymptotics of RelaxatioOscillations
3.1. Degenerate Systems
3.2. Systems of First Approximation
3.3. Normalizations of Fast-Slow Systems with Two Slow Variables for
3.4. Derivatioof the Systems of First Approximation
3.5. Investigatioof the Systems of First Approximation
3.6. Funnels
3.7. Periodic RelaxatioOscillations ithe Plane
4. Delayed Loss of Stability as a Pair of Eigenvalues Cross the Imaginary Axis
4.1. Generic Systems
4.2. Delayed Loss of Stability
4.3. Hard Loss of Stability iAnalytic Systems of Type 2
4.4. Hysteresis
4.5. The Mechanism of Delay
4.6. Computatioof the Moment of Jumping iAnalytic Systems
4.7. Delay UpoLoss of Stability by a Cycle
4.8. Delayed Loss of Stability and “Ducks” .
5. Duck Solutions
5.1. AExample: A Singular Point othe Fold of the Slow Surface
5.2. Existence of Duck Solutions
5.3. The Evolutioof Simple Degenerate Ducks
5.4. A Semi-local Phenomenon: Ducks with Relaxation
5.5. Ducks iR3 and Rn
Recommended Literature
References
Additional References
自然科学 数学 数学理论
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