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26 Result(s)
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Book
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Chapter
Stability of Equilibriums
In this chapter, basic concepts of nonlinear dynamical systems are introduced. A local theory of equilibrium stability for nonlinear dynamical systems is discussed. The spiral stability of equilibriums in nonl...
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Chapter
Low-Dimensional Dynamical Systems
In this chapter, low-dimensional nonlinear dynamical systems are discussed. The stability and bifurcations of the 1-dimensional systems are presented. The higher order singularity and stability for 1-dimension...
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Chapter
Low-Degree Polynomial Systems
In this chapter, the global stability and bifurcation of equilibriums in low-degree polynomial systems are discussed. Appearing and switching bifurcations of simple and higher order equilibriums are discussed,...
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Chapter
(2m+1)th-Degree Polynomial Systems
In this chapter, the global stability and bifurcations of equilibriums in the (2m+1)th-degree polynomial systems are discussed for a better understanding of the complexity of bifurcations and stability of equilib...
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Chapter
Bifurcations of Equilibrium
In this chapter, the hyperbolic bifurcations of equilibriums on the eigenvectors in nonlinear dynamical systems are discussed, and the Hopf bifurcation of an equilibrium on a specific eigenvector plane is pres...
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Chapter
Equilibrium Stability in 1-Dimensional Systems
In this chapter, a global analysis of equilibrium stability in 1-dimensional nonlinear dynamical systems is presented. The classification of dynamical systems is given first, and infinite-equilibrium systems a...
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Chapter
(2m)th-Degree Polynomial Systems
In this chapter, the global stability and bifurcations of equilibriums in the (2m)th-degree polynomial system are discussed for a better understanding of the complexity of bifurcations and stability of equilibriu...
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Chapter
Infinite-Equilibrium Systems
In this chapter, dynamical systems with infinite equilibriums are discussed through the local analysis. A method for equilibriums in nonlinear dynamical systems is developed. The generalized normal forms of no...
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Chapter
Correction to: Two-Dimensional Quadratic Nonlinear Systems
This book was inadvertently published with few errors. This has now been amended in respective chapters.
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Chapter
Linear-Bivariate Quadratic Dynamics
In this chapter, nonlinear dynamics of dynamical systems possessing linear-bivariate quadratic vector fields will be discussed. The dynamical systems with a constant vector field with a linear-bivariate quadra...
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Chapter
Nonlinear-Bivariate Quadratic Systems
In this chapter, nonlinear dynamics of dynamical systems possessing nonlinear-bivariate quadratic vector fields will be discussed. The dynamical systems with two linear bivariate product vector fields will be ...
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Chapter
Single-Linear-Bivariate Quadratic Systems
In this chapter, two-dimensional nonlinear systems possessing single-linear-bivariate quadratic vector fields are discussed, and the appearing and switching bifurcations for the 1-dimensional flows (e.g., up-p...
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Chapter
Linear-Bivariate Product Quadratic Systems
In this chapter, nonlinear dynamics of dynamical systems possessing linear-bivariate product quadratic vector fields will be discussed. The dynamical systems with two linear-bivariate quadratic vector fields w...
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Book
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Chapter
Two-Dimensional Linear-Bivariate Linear Systems
In this chapter, two-dimensional linear-bivariate linear systems are discussed. The single-linear-bivariate linear systems will be discussed first, and the switching bifurcations for the 1-dimensional flows (e...
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Book Series
Nonlinear Physical Science
Volume 0 / 2010
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Chapter
Single-Variable Quadratic Systems with a Self-Univariate Quadratic Vector Field
In this chapter, two-dimensional single-variable quadratic systems with a self-univariate quadratic vector field are discussed, and the appearing and switching bifurcations for the 1-dimensional flows (e.g., s...
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Chapter
Variable-Independent Quadratic Dynamics
In this chapter, nonlinear dynamics of dynamical systems possessing two variable-independent univariate vector fields is discussed. The dynamical systems with a constant vector field and a variable-independent...
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Book
