Nonlinear Physical Science
Volume 0 / 2010
Page
%P
52 Result(s)
within
Albert C. J. Luo
Complexity
Control and Systems Theory
Vibration, Dynamical Systems, Control
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Article
To infinitely many spiral homoclinic orbits from periodic motions in the Lorenz system
In this paper, the grape cluster routes of periodic motions to spiral homoclinic orbits in the Lorenz system is studied by the discrete map** method. On the grape cluster of the bifurcation routes, periodic ...
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Book Series
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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
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Chapter
Two-Univariate Product Quadratic Systems
In this chapter, nonlinear dynamics of dynamical systems possessing bivariate quadratic vector fields is discussed as in Luo (Journal of Vibration Testing and System Dynamics in 2023). The bivariate quadratic vec...
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Chapter
Product-Bivariate Quadratic Systems with a Non-Self-Univariate Quadratic Vector Field
In this chapter, nonlinear dynamics of dynamical systems possessing a bivariate product quadratic vector field and a non-self-univariate quadratic vector field is discussed as in Luo (J Vib Test Syst Dyn, 2023). ...
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Chapter
Two-Dimensional Linear Dynamical Systems
In this Chapter, two-dimensional dynamical systems with constant and linear vector fields are discussed. Dynamical systems with one-variable vector fields are presented and the singular dynamics of two-dimensi...
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Chapter
Single-Variable Quadratic Systems with a Non-Self-Univariate Quadratic Vector Field
In this chapter, two-dimensional, single-variable quadratic systems with a non-self-univariate quadratic vector fields are discussed, and the appearing and switching bifurcations for the 1-dimensional flows (e...
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Chapter
Variable-Crossing Univariate Quadratic Systems
In this chapter, nonlinear dynamics of dynamical systems with two variable-crossing univariate vector fields is discussed. The dynamical systems with a constant vector field and a variable-crossing univariate ...
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Chapter
Product-Bivariate Quadratic Systems with a Self-Univariate Quadratic Vector Field
In this chapter, nonlinear dynamics of dynamical systems possessing a bivariate product vector field and a self-univariate quadratic vector field is discussed as in Luo (J Vib Test Syst Dyn, 2023). The stability ...
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Article
Bifurcation dynamics of complex period-1 motions to chaos in an electromagnetically tuned duffing oscillator
In this paper, bifurcation dynamics of periodic motions in the electromagnetically tuned Duffing oscillator are studied through symmetric period-1 to asymmetric period-2 motions. On the bifurcation routes, the...
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Article
Sequential symmetric periodic motions in a symmetric discontinuous dynamical system
In this paper, grazing-induced sequential symmetric periodic motions in a symmetric discontinuous dynamical system with a symmetric hyperbolic boundary are studied analytically. The analytical switching condit...
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Article
Periodic cutting motions in a vibration-assisted, regenerative, nonlinear Orthogonal turning system
In this paper, a mathematical model of 2-degrees-of-freedom (2-DOF), vibration-assisted, regenerative, nonlinear orthogonal turning system is developed. The period-1 motions of such a system are predicted thro...
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Article
Periodic motions on bifurcation trees in an inverted pendulum with a periodically moving base
This paper studies periodic motions of an inverted pendulum with a periodically moving base. A bifurcation tree of period-1 to period-8 motions is predicted through a discrete implicit map** method. The stab...
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Article
Analytical periodic motions in a discontinuous system with a switching hyperbola
In this paper, studied are periodic motions in a discontinuous system with three vector fields switching through two branches of a hyperbola. The switchability conditions of flows at the discontinuous boundari...
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Article
On bifurcations and local stability in 1-D nonlinear discrete dynamical systems
In this paper, a theory of bifurcations and local stability of fixed-points (or period-1 solutions) in one-dimensional nonlinear discrete dynamical systems is presented. The linearized discrete dynamical syste...
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Article
An independent period-3 motion to chaos in a nonlinear flexible rotor system
In this paper, a bifurcation tree of an independent period-3 motion to chaos in a flexible nonlinear rotor system is developed semi-analytically. The period-3 motion was traditionally called the subharmonic pe...
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Article
On period-1 motions to chaos in a 1-dimensional, time-delay, nonlinear system
In this paper, bifurcation trees of period-1 motions to chaos in a 1-dimensional, time-delay, nonlinear system are investigated. For time-delay terms of non-polynomial functions, the traditional analytical met...
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Article
On dynamics of infinite-equilibrium systems
In this paper, dynamical systems with infinite-equilibriums is discussed through the local analysis. A computational method for equilibriums in nonlinear dynamical systems is developed which extends the Newton...
