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Two-dimensional Product Cubic Systems, Vol. VII : Self- Quadratic Vector Fields / by Albert C. J. Luo.
- Format:
- Book
- Author/Creator:
- Luo, Albert C. J., author.
- Language:
- English
- Subjects (All):
- Multibody systems.
- Vibration.
- Mechanics, Applied.
- Dynamics.
- Nonlinear theories.
- Stochastic analysis.
- Multibody Systems and Mechanical Vibrations.
- Applied Dynamical Systems.
- Engineering Mechanics.
- Stochastic Analysis.
- Local Subjects:
- Multibody Systems and Mechanical Vibrations.
- Applied Dynamical Systems.
- Engineering Mechanics.
- Stochastic Analysis.
- Physical Description:
- 1 online resource (240 pages)
- Edition:
- 1st ed. 2024.
- Place of Publication:
- Cham : Springer Nature Switzerland : Imprint: Springer, 2024.
- Summary:
- This book, the seventh of 15 related monographs, concerns nonlinear dynamics and singularity of cubic dynamical systems possessing a product-cubic vector field and a self-univariate quadratic vector field. The equilibrium singularity and bifurcation dynamics are discussed. The saddle-source (sink) is the appearing bifurcations for saddle and source (sink). The double-saddle equilibriums are the appearing bifurcations of the saddle-source and saddle-sink, and also the appearing bifurcations of the network of saddles, sink and source. The infinite-equilibriums for the switching bifurcations include: • inflection-saddle infinite-equilibriums, • hyperbolic-source (sink) infinite-equilibriums, • up-down (down-up) saddle infinite-equilibriums, • inflection-source (sink) infinite-equilibriums. Develops a theory of cubic dynamical systems possessing a product-cubic vector field and a self-quadratic vector field; Finds series/networks of equilibriums, 1-dimenional hyperbolic/hyperbolic-secant flows, finite-equilibrium switching; Presents sink and source separated by a connected hyperbolic-secant flow, and the (SO,SI) and (SI,SO)-saddles. .
- Contents:
- Chapter 1: Self-quadratic and product-cubic Systems
- Chapter 2: Saddle-node singularity and bifurcation dynamics
- Chapter 3: Double-saddles and switching bifurcations.
- Notes:
- Includes index.
- ISBN:
- 3-031-48483-5
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