scholarly journals A discrete dynamics approach to interbank financial contagion

2021 ◽  
Author(s):  
John Leventides ◽  
Costas Poulios ◽  
Elias Camouzis
Keyword(s):  
Dynamical Systems ◽  
Linear Operator ◽  
Mathematical Models ◽  
Systems Theory ◽  
Mathematical Description ◽  
Financial Networks ◽  
Financial Contagion ◽  
Discrete Dynamics ◽  
New Framework

Abstract The purpose of this paper is to describe in terms of mathematical models and systems theory the dynamics of interbank financial contagion. Such a description gives rise to a model that can be studied with mathematical tools and will provide a new framework for the study of contagion dynamics complementary to research by simulation studied so far. It provides a better understanding of such financial networks and a unifying network for the research of financial contagion. The mathematical description we present is in terms of Boolean dynamical systems and a linear operator. We relate the properties of the dynamical systems to the properties of the operator.

scholarly journals Some elements for a history of the dynamical systems theory

2021 ◽  
Vol 31 (5) ◽  
pp. 053110
Author(s):  
Christophe Letellier ◽  
Ralph Abraham ◽  
Dima L. Shepelyansky ◽  
Otto E. Rössler ◽  
Philip Holmes ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
History Of

scholarly journals The Dynamics of Musical Participation

2021 ◽  
pp. 102986492098831
Author(s):  
Andrea Schiavio ◽  
Pieter-Jan Maes ◽  
Dylan van der Schyff
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Dynamical Systems Theory ◽  
Coordination Dynamics ◽  
Musical Experience ◽  
The Core ◽  
Interactive Dynamics ◽  
Interdisciplinary Scholarship ◽  
Core Features

In this paper we argue that our comprehension of musical participation—the complex network of interactive dynamics involved in collaborative musical experience—can benefit from an analysis inspired by the existing frameworks of dynamical systems theory and coordination dynamics. These approaches can offer novel theoretical tools to help music researchers describe a number of central aspects of joint musical experience in greater detail, such as prediction, adaptivity, social cohesion, reciprocity, and reward. While most musicians involved in collective forms of musicking already have some familiarity with these terms and their associated experiences, we currently lack an analytical vocabulary to approach them in a more targeted way. To fill this gap, we adopt insights from these frameworks to suggest that musical participation may be advantageously characterized as an open, non-equilibrium, dynamical system. In particular, we suggest that research informed by dynamical systems theory might stimulate new interdisciplinary scholarship at the crossroads of musicology, psychology, philosophy, and cognitive (neuro)science, pointing toward new understandings of the core features of musical participation.

scholarly journals Coevolving institutions and the paradox of informal constraints

2021 ◽  
pp. 1-20
Author(s):  
Daniel Seligson ◽  
Anne E. C. McCants
Keyword(s):  
Economic Growth ◽  
Game Theory ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Institutional Economics ◽  
Dynamical Systems Theory ◽  
New Institutional Economics ◽  
Long Run

Abstract We can all agree that institutions matter, though as to which institutions matter most, and how much any of them matter, the matter is, paraphrasing Douglass North's words at the Nobel podium, unresolved after seven decades of immense effort. We suggest that the obstacle to progress is the paradigm of the New Institutional Economics itself. In this paper, we propose a new theory that is: grounded in institutions as coevolving sources of economic growth rather than as rules constraining growth; and deployed in dynamical systems theory rather than game theory. We show that with our approach some long-standing problems are resolved, in particular, the paradoxical and perplexingly pervasive influence of informal constraints on the long-run character of economies.

scholarly journals Category Theory for Autonomous and Networked Dynamical Systems

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 302 ◽  
Author(s):  
Jean-Charles Delvenne
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Ergodic Theory ◽  
Category Theory ◽  
Open Systems ◽  
Topological Dynamics ◽  
Control Problems ◽  
Natural Conditions ◽  
Discussion Paper ◽  
Open Systems Theory

In this discussion paper we argue that category theory may play a useful role in formulating, and perhaps proving, results in ergodic theory, topogical dynamics and open systems theory (control theory). As examples, we show how to characterize Kolmogorov–Sinai, Shannon entropy and topological entropy as the unique functors to the nonnegative reals satisfying some natural conditions. We also provide a purely categorical proof of the existence of the maximal equicontinuous factor in topological dynamics. We then show how to define open systems (that can interact with their environment), interconnect them, and define control problems for them in a unified way.

scholarly journals Stability analysis and controller synthesis for hybrid dynamical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4937-4960 ◽  
Author(s):  
W. P. M. H. Heemels ◽  
B. De Schutter ◽  
J. Lunze ◽  
M. Lazar
Keyword(s):  
Dynamical Systems ◽  
Mathematical Models ◽  
Hybrid Systems ◽  
Discrete Event ◽  
Research Area ◽  
Hybrid Dynamical Systems ◽  
Technological Systems ◽  
Analysis And Synthesis ◽  
Control Community ◽  
The One

Wherever continuous and discrete dynamics interact, hybrid systems arise. This is especially the case in many technological systems in which logic decision-making and embedded control actions are combined with continuous physical processes. Also for many mechanical, biological, electrical and economical systems the use of hybrid models is essential to adequately describe their behaviour. To capture the evolution of these systems, mathematical models are needed that combine in one way or another the dynamics of the continuous parts of the system with the dynamics of the logic and discrete parts. These mathematical models come in all kinds of variations, but basically consist of some form of differential or difference equations on the one hand and automata or other discrete-event models on the other hand. The collection of analysis and synthesis techniques based on these models forms the research area of hybrid systems theory, which plays an important role in the multi-disciplinary design of many technological systems that surround us. This paper presents an overview from the perspective of the control community on modelling, analysis and control design for hybrid dynamical systems and surveys the major research lines in this appealing and lively research area.

scholarly journals On attracting sets in artificial networks: cross activation

2018 ◽  
Vol 16 ◽  
pp. 01005
Author(s):  
Felix Sadyrbaev
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Mathematical Models ◽  
Ordinary Differential Equations ◽  
Critical Points ◽  
Regulatory Networks ◽  
Main Diagonal ◽  
Sigmoidal Function ◽  
Genomic Regulatory Networks ◽  
Over Time

Mathematical models of artificial networks can be formulated in terms of dynamical systems describing the behaviour of a network over time. The interrelation between nodes (elements) of a network is encoded in the regulatory matrix. We consider a system of ordinary differential equations that describes in particular also genomic regulatory networks (GRN) and contains a sigmoidal function. The results are presented on attractors of such systems for a particular case of cross activation. The regulatory matrix is then of particular form consisting of unit entries everywhere except the main diagonal. We show that such a system can have not more than three critical points. At least n–1 eigenvalues corresponding to any of the critical points are negative. An example for a particular choice of sigmoidal function is considered.

On the Roughness of Quasinilpotency Property of One-parameter Semigroups

2017 ◽  
Vol 60 (2) ◽  
pp. 364-371 ◽  
Author(s):  
Ciprian Preda
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Infinitesimal Generator ◽  
Autonomous Systems ◽  
Dynamical Systems Theory ◽  
Extinction Property ◽  
Quasinilpotent Operators ◽  
Strong Concept ◽  
Time Extinction

AbstractLet S := {S(t)}t≥0 be a C0-semigroup of quasinilpotent operators (i.e., σ(S(t)) = {0} for eacht> 0). In dynamical systems theory the above quasinilpotency property is equivalent to a very strong concept of stability for the solutions of autonomous systems. This concept is frequently called superstability and weakens the classical ûnite time extinction property (roughly speaking, disappearing solutions). We show that under some assumptions, the quasinilpotency, or equivalently, the superstability property of a C0-semigroup is preserved under the perturbations of its infinitesimal generator.

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