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.

MODELING LINEAR DYNAMICAL SYSTEMS BY CONTINUOUS-VALUED CELLULAR AUTOMATA

2007 ◽  
Vol 18 (05) ◽  
pp. 833-848 ◽  
Author(s):  
JUAN CARLOS SECK TUOH MORA ◽  
MANUEL GONZALEZ HERNANDEZ ◽  
NORBERTO HERNANDEZ ROMERO ◽  
AARON RODRIGUEZ TREJO ◽  
SERGIO V. CHAPA VERGARA
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Linear Systems ◽  
Configuration Space ◽  
Integration Method ◽  
Numerical Calculations ◽  
Linear Dynamical Systems ◽  
Original Part

This paper exposes a procedure for modeling and solving linear systems using continuous-valued cellular automata. The original part of this work consists on showing how the cells in the automaton may contain both real values and operators for carrying out numerical calculations and solve a desired problem. In this sense the automaton acts as a program, where data and operators are mixed in the evolution space for obtaining the correct calculations. As an example, Euler's integration method is implemented in the configuration space in order to achieve an approximated solution for a dynamical system. Three examples showing linear behaviors are presented.

scholarly journals A unified approach for sparse dynamical system inference from temporal measurements

2018 ◽  
Vol 35 (18) ◽  
pp. 3387-3396 ◽  
Author(s):  
Yannis Pantazis ◽  
Ioannis Tsamardinos
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Single Cell ◽  
Time Course ◽  
Cell Mass ◽  
Supplementary Information ◽  
Unified Approach ◽  
Unknown Parameters ◽  
Inference Problem ◽  
Linear Dynamical Systems

Abstract Motivation Temporal variations in biological systems and more generally in natural sciences are typically modeled as a set of ordinary, partial or stochastic differential or difference equations. Algorithms for learning the structure and the parameters of a dynamical system are distinguished based on whether time is discrete or continuous, observations are time-series or time-course and whether the system is deterministic or stochastic, however, there is no approach able to handle the various types of dynamical systems simultaneously. Results In this paper, we present a unified approach to infer both the structure and the parameters of non-linear dynamical systems of any type under the restriction of being linear with respect to the unknown parameters. Our approach, which is named Unified Sparse Dynamics Learning (USDL), constitutes of two steps. First, an atemporal system of equations is derived through the application of the weak formulation. Then, assuming a sparse representation for the dynamical system, we show that the inference problem can be expressed as a sparse signal recovery problem, allowing the application of an extensive body of algorithms and theoretical results. Results on simulated data demonstrate the efficacy and superiority of the USDL algorithm under multiple interventions and/or stochasticity. Additionally, USDL’s accuracy significantly correlates with theoretical metrics such as the exact recovery coefficient. On real single-cell data, the proposed approach is able to induce high-confidence subgraphs of the signaling pathway. Availability and implementation Source code is available at Bioinformatics online. USDL algorithm has been also integrated in SCENERY (http://scenery.csd.uoc.gr/); an online tool for single-cell mass cytometry analytics. Supplementary information Supplementary data are available at Bioinformatics online.

scholarly journals Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems

1989 ◽  
Vol 31 (1) ◽  
pp. 48-75 ◽  
Author(s):  
A. J. Roberts
Keyword(s):  
Dynamical System ◽  
Invariant Manifold ◽  
Initial Conditions ◽  
Long Term Evolution ◽  
Equation Model ◽  
Starting Position ◽  
System A ◽  
Term Evolution ◽  
Shear Dispersion

AbstractA centre manifold or invariant manifold description of the evolution of a dynamical system provides a simplified view of the long term evolution of the system. In this work, I describe a procedure to estimate the appropriate starting position on the manifold which best matches an initial condition off the manifold. I apply the procedure to three examples: a simple dynamical system, a five-equation model of quasi-geostrophic flow, and shear dispersion in a channel. The analysis is also relevant to determining how best to account, within the invariant manifold description, for a small forcing in the full system.

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 STABILITY OF NON-LINEAR DYNAMICAL SYSTEM

2021 ◽  
Vol 9 (07) ◽  
pp. 275-283
Author(s):  
Anas Salim Youns ◽  
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Linear System ◽  
Three Dimension ◽  
Linear Dynamical System ◽  
Linear Dynamical Systems ◽  
Linearization Technique ◽  
The Public ◽  
Non Linear ◽  
The Stability

The mainobjective of this research is to study the stability of thenon-lineardynamical system by using the linearization technique of three dimension systems toobtain an approximate linear system and find its stability. We apply this technique to reaches to the stability of the public non linear dynamical systems of dimension. Finally, some proposed examples (example (1) and example (2)) are given to explain this technique and used the corollary.

Linear dynamical systems of dimension two over the ring of integers modulo pt

2020 ◽  
Vol 12 (06) ◽  
pp. 2050074
Author(s):  
Yangjiang Wei ◽  
Heyan Xu ◽  
Linhua Liang
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Diagonal Matrix ◽  
Linear Dynamical System ◽  
Linear Dynamical Systems ◽  
Ring Of Integers ◽  
Idempotent Matrix ◽  
Nilpotent Matrix ◽  
Matrix Formula

In this paper, we investigate the linear dynamical system [Formula: see text], where [Formula: see text] is the ring of integers modulo [Formula: see text] ([Formula: see text] is a prime). In order to facilitate the visualization of this system, we associate a graph [Formula: see text] on it, whose nodes are the points of [Formula: see text], and for which there is an arrow from [Formula: see text] to [Formula: see text], when [Formula: see text] for a fixed [Formula: see text] matrix [Formula: see text]. In this paper, the in-degree of each node in [Formula: see text] is obtained, and a complete description of [Formula: see text] is given, when [Formula: see text] is an idempotent matrix, or a nilpotent matrix, or a diagonal matrix. The results in this paper generalize Elspas’ [1959] and Toledo’s [2005].

Phase Space Reconstruction

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Dynamical Systems ◽  
Statistical Mechanics ◽  
State Space ◽  
Phase Plane ◽  
Material Point ◽  
The Other ◽  
Straight Line ◽  
Mathematical Construction

In this chapter we introduce an important concept concerning the study of both discrete and continuous dynamical systems, the concept of phase space or “state space”. It is an abstract mathematical construction with important applications in statistical mechanics, to represent the time evolution of a dynamical system in geometric shape. This space has as many dimensions as the number of variables needed to define the instantaneous state of the system. For instance, the state of a material point moving on a straight line is defined by its position and velocity at each instant, so that the phase space for this system is a plane in which one axis is the position and the other one the velocity. In this case, the phase space is also called “phase plane”. It is later applied in many chapters of the book.

On the Dynamical Systems Stability Control and Applications

2014 ◽  
Vol 555 ◽  
pp. 361-368
Author(s):  
Marcel Migdalovici ◽  
Daniela Baran ◽  
Gabriela Vlădeanu
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Nonlinear System ◽  
Stability Control ◽  
Necessary Condition ◽  
Linear Dynamical Systems ◽  
System A ◽  
First Approximation ◽  
Free Parameters ◽  
The Stability

The stability control analyzed by us, in this show, is based on our results in the domain of dynamical systems that depend of parameters. Any dynamical system can be considered as dynamical system that depends of parameters, without numerical particularization of them. All concrete dynamical systems, meted in the specialized literature, underline the property of separation between the stable and unstable zones, in sense of Liapunov, for two free parameters. This property can be also seen for one or more free parameters. Some mathematical conditions of separation between stable and unstable zones for linear dynamical systems are identified by us. For nonlinear systems, the conditions of separation may be identified using the linear system of first approximation attached to nonlinear system. A necessary condition of separation between stable and unstable zones, identified by us, is the sufficient order of differentiability or conditions of continuity for the functions that define the dynamical system. The property of stability zones separation can be used in defining the strategy of stability assurance and optimizing of the parameters, in the manner developed in the paper. The cases of dynamical systems that assure the separations of the stable and unstable zones, in your evolution, and permit the stability control, are analyzed in the paper.

scholarly journals Reflections on Termination of Linear Loops

2021 ◽  
pp. 51-74
Author(s):  
Shaowei Zhu ◽  
Zachary Kincaid
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Transition System ◽  
Linear Dynamical System ◽  
Linear Dynamical Systems ◽  
Termination Analysis ◽  
Integer Arithmetic ◽  
Transition Formula

AbstractThis paper shows how techniques for linear dynamical systems can be used to reason about the behavior of general loops. We present two main results. First, we show that every loop that can be expressed as a transition formula in linear integer arithmetic has a best model as a deterministic affine transition system. Second, we show that for any linear dynamical system f with integer eigenvalues and any integer arithmetic formula G, there is a linear integer arithmetic formula that holds exactly for the states of f for which G is eventually invariant. Combining the two, we develop a monotone conditional termination analysis for general loops.

Sign in / Sign up

Export Citation Format

Share Document