Discontinuity-induced bifurcations of piecewise smooth dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4915-4935 ◽  
Author(s):  
M. di Bernardo ◽  
S. J. Hogan
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Limit Cycles ◽  
State Of The Art ◽  
Piecewise Smooth ◽  
Hybrid Dynamical Systems ◽  
Current State ◽  
Relevant Class

This paper presents an overview of the current state of the art in the analysis of discontinuity-induced bifurcations (DIBs) of piecewise smooth dynamical systems, a particularly relevant class of hybrid dynamical systems. Firstly, we present a classification of the most common types of DIBs involving non-trivial interactions of fixed points and equilibria of maps and flows with the manifolds in phase space where the system is non-smooth. We then analyse the case of limit cycles interacting with such manifolds, presenting grazing and sliding bifurcations. A description of possible classification strategies to predict and analyse the scenarios following such bifurcations is also discussed, with particular attention to those methodologies that can be applied to generic n -dimensional systems.

scholarly journals Unidades de traducción culturalmente marcadas: propuesta de clasificación dinámica con fines traductológicos

2018 ◽  
pp. 193-213
Author(s):  
Inma Mendoza García
Keyword(s):  
Critical Analysis ◽  
Scientific Literature ◽  
State Of The Art ◽  
Target System ◽  
Translation Process ◽  
Current State ◽  
Translation Practice ◽  
Dynamic Perspective ◽  
Level Of Knowledge

In the context of Translation Studies, this paper presents a proposal for classifying culturally marked translation units from a functional dynamic perspective that is considered to be more useful for both translation practice and translation-related research than other taxonomies so far suggested by the majority of theorists. For this purpose, first I provide an overview of the current state of the art in research on these specific translation units with regard to their designation, concept and classification. Second, I conduct a critical analysis of the heterogeneity of designations and definitions as well as of the static taxonomies so far prevailing in scientific literature in this respect. Third, I select a designation for these sorts of units and justify the decision made. Fourth, I provide a detailed description of the concept and its nature. Finally, I design a classificatory model that is not based on a mere classification of culture-related areas and topics but takes into account all the intratextual and extratextual factors involved in the translation process. The proposal put forward is guided by two main parameters: the degree of lingüistic and cultural (in)equivalence between the source system and the target system and the level of knowledge the reader is supposed to possess about the culturally marked textual units.

scholarly journals Use of a Novel Grammatical Inference Approach in Classification of Amyloidogenic Hexapeptides

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Wojciech Wieczorek ◽  
Olgierd Unold
Keyword(s):  
Support Vector Machine ◽  
Correlation Coefficient ◽  
State Of The Art ◽  
Superior Performance ◽  
Support Vector ◽  
Grammatical Inference ◽  
Regular Expressions ◽  
Inference Algorithm ◽  
Current State

The present paper is a novel contribution to the field of bioinformatics by using grammatical inference in the analysis of data. We developed an algorithm for generating star-free regular expressions which turned out to be good recommendation tools, as they are characterized by a relatively high correlation coefficient between the observed and predicted binary classifications. The experiments have been performed for three datasets of amyloidogenic hexapeptides, and our results are compared with those obtained using the graph approaches, the current state-of-the-art methods in heuristic automata induction, and the support vector machine. The results showed the superior performance of the new grammatical inference algorithm on fixed-length amyloid datasets.

scholarly journals THE STRUCTURE OF PHASE SPACE CLOSE TO FIXED POINTS IN A 4D SYMPLECTIC MAP

2013 ◽  
Vol 23 (07) ◽  
pp. 1330023 ◽  
Author(s):  
L. ZACHILAS ◽  
M. KATSANIKAS ◽  
P. A. PATSIS
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Periodic Orbits ◽  
Hamiltonian Systems ◽  
Symplectic Map ◽  
Rotation Method ◽  
Good Agreement

We study the dynamics in the neighborhood of fixed points in a 4D symplectic map by means of the color and rotation method. We compare the results with the corresponding cases encountered in galactic type potentials and we find that they are in good agreement. The fact that the 4D phase space close to fixed points is similar to the 4D representations of the surfaces of section close to periodic orbits, indicates an archetypical 4D pattern for each kind of (in)stability, not only in 3D autonomous Hamiltonian systems with galactic type potentials but for a larger class of dynamical systems. This pattern is successfully visualized with the method we use in the paper.

NULLCLINES AND NULLCLINE INTERSECTIONS

2006 ◽  
Vol 16 (10) ◽  
pp. 3023-3033 ◽  
Author(s):  
RENÉ THOMAS
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Differential Equations ◽  
Fixed Points ◽  
Ordinary Differential Equations ◽  
Chaotic Dynamics ◽  
Jacobian Matrix ◽  
Steady States ◽  
Sustained Oscillations ◽  
Sign Patterns

One purpose of this paper is to document the fact that, in dynamical systems described by ordinary differential equations, the trajectories can be organized not only around fixed points (steady states), but also around lines. In 2D, these lines are the nullclines themselves, in 3D, the intersections of the nullclines two by two, etc.We precise the concepts of "partial steady states" (i.e. steady states in a subsystem that consists of sections of phase space by planes normal to one of the axes) and of "partial multistationarity" (multistationarity in such a subsystem).Steady states, nullclines or their intersections are revisited in terms of circuits, defined from nonzero elements of the Jacobian matrix. It is shown how the mere examination of the Jacobian matrix and the sign patterns of its circuits can help interpreting (and often predicting) aspects of the dynamics of systems.The results reinforce the idea that chaotic dynamics requires both a positive circuit, to provide (if only partial) multistationarity, and a negative circuit, to provide sustained oscillations. As shown elsewhere, a single circuit may suffice if it is ambiguous (i.e. positive or negative depending on the location in phase space).The description in terms of circuits is by no means exclusive of the classical description. In many cases, a fruitful approach involves repeated feedback between the two viewpoints.

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