An Instability Theorem for Steady Motions in Free and Restrained Dynamical Systems

1980 ◽  
Vol 47 (4) ◽  
pp. 908-912 ◽  
Author(s):  
P. Hagedorn ◽  
W. Teschner
Keyword(s):  
Dynamical Systems ◽  
Stability Behavior ◽  
Two Systems ◽  
The Stability ◽  
Steady Motions

The stability of steady motions in dynamical systems with ignorable coordinates is considered. In addition to the original “free” systems “restrained” systems are defined in such a way that the ignorable velocities remain constant along all motions; the stability behavior of the two systems is compared. A previously established instability theorem is generalized and three examples are given.

On the Stability of Steady Motions in Free and Restrained Dynamical Systems

1979 ◽  
Vol 46 (2) ◽  
pp. 427-432 ◽  
Author(s):  
P. Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Stability Behavior ◽  
Stability And Instability ◽  
Heavy Gyrostat ◽  
The Stability ◽  
Steady Motions

In this paper the stability of the steady motions of dynamical systems with ignorable coordinates is considered. In addition to the original “free” systems “restrained” systems are defined in such a way that the ignorable velocities remain constant for all motions. The relation between the stability behavior of these two types of systems is examined in detail and several stability and instability theorems are given for damped and undamped systems. An illustrative example deals with the steady motions of a heavy gyrostat.

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.

scholarly journals Analysis of an Ecoepidemiological Model with Prey Refuges

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Shufan Wang ◽  
Zhihui Ma
Keyword(s):  
Functional Response ◽  
Contact Process ◽  
Global Perspective ◽  
Basic System ◽  
Stability Behavior ◽  
The Stability ◽  
Holling Iii Functional Response ◽  
Disease In Prey ◽  
Prey Refuges

An ecoepidemiological system with prey refuges and disease in prey is proposed. Bilinear incidence and Holling III functional response are used to model the contact process and the predation process, respectively. We will study the stability behavior of the basic system from a local to a global perspective. Permanence of the considered system is also investigated.

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