On the Stability of Toroidal Manifold for One Class of Dynamical Systems

2017 ◽  
Vol 228 (3) ◽  
pp. 314-322
Author(s):  
M. M. Perestyuk ◽  
Yu. M. Perestyuk
Keyword(s):  
Dynamical Systems ◽  
Toroidal Manifold ◽  
The Stability

scholarly journals The Stability Criteria with Compound Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yazhuo Zhang ◽  
Baodong Zheng
Keyword(s):  
Dynamical Systems ◽  
Spectral Property ◽  
Discrete Dynamical Systems ◽  
Asymptotical Stability ◽  
Hopf Bifurcations ◽  
Stability Criteria ◽  
Bifurcation Problem ◽  
Compound Matrices ◽  
The Stability ◽  
Schur Stability

The bifurcation problem is one of the most important subjects in dynamical systems. Motivated by M. Li et al. who used compound matrices to judge the stability of matrices and the existence of Hopf bifurcations in continuous dynamical systems, we obtained some effective methods to judge the Schur stability of matrices on the base of the spectral property of compound matrices, which can be used to judge the asymptotical stability and the existence of Hopf bifurcations of discrete dynamical systems.

A novel approach for the stability problem in non-linear dynamical systems

2003 ◽  
Vol 155 (1) ◽  
pp. 21-30 ◽  
Author(s):  
Tarcı́sio M. Rocha Filho ◽  
Iram M. Gléria ◽  
Annibal Figueiredo
Keyword(s):  
Dynamical Systems ◽  
Stability Problem ◽  
Linear Dynamical Systems ◽  
Novel Approach ◽  
Non Linear ◽  
The Stability

SINGULARITY, SWITCHABILITY AND BIFURCATIONS IN A 2-DOF, PERIODICALLY FORCED, FRICTIONAL OSCILLATOR

2013 ◽  
Vol 23 (03) ◽  
pp. 1330009 ◽  
Author(s):  
ALBERT C. J. LUO ◽  
MOZHDEH S. FARAJI MOSADMAN
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Analysis ◽  
Degrees Of Freedom ◽  
Eigenvalue Analysis ◽  
Analytical Dynamics ◽  
Periodic Motions ◽  
Stability And Bifurcation ◽  
Mapping Structures ◽  
Stability And Bifurcation Analysis ◽  
The Stability

In this paper, the analytical dynamics for singularity, switchability, and bifurcations of a 2-DOF friction-induced oscillator is investigated. The analytical conditions of the domain flow switchability at the boundaries and edges are developed from the theory of discontinuous dynamical systems, and the switchability conditions of boundary flows from domain and edge flows are presented. From the singularity and switchability of flow to the boundary, grazing, sliding and edge bifurcations are obtained. For a better understanding of the motion complexity of such a frictional oscillator, switching sets and mappings are introduced, and mapping structures for periodic motions are adopted. Using an eigenvalue analysis, the stability and bifurcation analysis of periodic motions in the friction-induced system is carried out. Analytical predictions and parameter maps of periodic motions are performed. Illustrations of periodic motions and the analytical conditions are completed. The analytical conditions and methodology can be applied to the multi-degrees-of-freedom frictional oscillators in the same fashion.

Large-Scale Uncertain Systems Under Insufficient Decentralized Controllers

1989 ◽  
Vol 111 (3) ◽  
pp. 359-363 ◽  
Author(s):  
Y. H. Chen
Keyword(s):  
Dynamical Systems ◽  
Uncertain Systems ◽  
Large Scale ◽  
Large Scale System ◽  
Uncertain Dynamical Systems ◽  
Partial Stability ◽  
Decentralized Controllers ◽  
Total Stability ◽  
The Stability

We consider a class of large-scale uncertain dynamical systems under decentralized controllers. The system is composed of N interconnected subsystems which possess uncertainty. Moreover, there are uncertainties in the interconnections. If the subsystems are under sufficient decentralized controllers, the large-scale system is practically stable. As certain controllers fail, study on the conditions for total stability of partial stability to be preserved is made. It can be shown that the stability is only related to bound of uncertainty and the structure of the large-scale system. Moreover, the conditions can be utilized to determine the importance of some controllers for stability.

Periodic Motions in an Autonomous System With a Discontinuous Vector Field

2020 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Parameter Study ◽  
Spring Stiffness ◽  
Algebraic Equations ◽  
Periodic Motions ◽  
Mapping Structures ◽  
The Stability

Abstract In this paper, periodic motions in an autonomous system with a discontinuous vector field are discussed. The periodic motions are obtained by constructing a set of algebraic equations based on motion mapping structures. The stability of periodic motions is investigated through eigenvalue analysis. The grazing bifurcations are presented by varying the spring stiffness. Once the grazing bifurcation occurs, periodic motions switches from the old motion to a new one. Numerical simulations are conducted for motion illustrations. The parameter study helps one understand autonomous discontinuous dynamical systems.

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
Chee Seng Chan ◽  
Dumitur Baleanu
Keyword(s):  
Dynamical Systems ◽  
Stability And Convergence ◽  
Uncertain Parameters ◽  
Crucial Issue ◽  
Computational Costs ◽  
First Order ◽  
Wide Range ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Fuzzy Dynamical Systems

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

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