scholarly journals Analysis of the practical stability and sensitivity of linear dynamical systems with change of phase space measurability

2016 ◽  
Vol 0 (3) ◽  
pp. 86-100
Author(s):  
Fedir G. Garashenko ◽  
Olga L. Soproniyk
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Practical Stability ◽  
Linear Dynamical Systems

FRACTALS AND CLOSURES OF LINEAR DYNAMICAL SYSTEMS EXCITED STOCHASTICALLY BY TEMPORAL INPUTS

2001 ◽  
Vol 11 (03) ◽  
pp. 755-779 ◽  
Author(s):  
RYOICHI WADA ◽  
KAZUTOSHI GOHARA
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Vector Fields ◽  
Invariant Set ◽  
Poincaré Section ◽  
Poincare Section ◽  
Linear Dynamical Systems ◽  
Cylindrical Phase ◽  
Iterated Functions ◽  
Cylindrical Phase Space

Fractals and closures of two-dimensional linear dynamical systems excited by temporal inputs are investigated. The continuous dynamics defined by the set of vector fields in the cylindrical phase space is reduced to the discrete dynamics defined by the set of iterated functions on the Poincaré section. When all iterated functions are contractions, it has already been shown theoretically that a trajectory in the cylindrical phase space converges into an attractive invariant set with a fractal-like structure. Calculating analytically the Lipschitz constants of iterated functions, we show that, under some conditions, noncontractions often appear. However, we numerically show that, even for noncontractions, an attractive invariant set with a fractal-like structure exists. By introducing the interpolating system, we can also show that the set of trajectories in the cylindrical phase space is enclosed by the tube structure whose initial set is the closure of the fractal set on the Poincaré section.

scholarly journals Dynamical tools for the analysis of long term evolution of volcanic tremor at Stromboli

1999 ◽  
Vol 42 (3) ◽  
Author(s):  
R. Carniel ◽  
M. Di Cecca
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Volcanic Tremor ◽  
Discrete Events ◽  
Strombolian Activity ◽  
Linear Dynamical Systems ◽  
Term Evolution ◽  
Extract Information

Stromboli is characterized by persistent seismic activity, both in terms of tremor and of discrete events associated with moderate explosions defining the so-called "Strombolian activity". This kind of permanent activity suggests the probable existence of a dynamical system governing the volcano. The purpose of this paper is to extract information on the "Stromboli dynamical system" from the seismic recordings. The analysis is carried out using the theory of non-linear dynamical systems and the delayed coordinates phase-space reconstruction. Several methods are presented and discussed in order to analyze volcanic tremor data in this framework; finally the time evolution of the computed parameters, both in the long term and close in time to paroxysmal phases, is presented and discussed. Evidence for a strong deterministic component in the dynamics of the volcano is shown.

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