Networked Systems Theory: Distributed Algorithms for Optimal Cooperation of Dynamical Systems

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.

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Coevolving institutions and the paradox of informal constraints

Journal of Institutional Economics ◽

10.1017/s1744137420000600 ◽

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.

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Category Theory for Autonomous and Networked Dynamical Systems

Entropy ◽

10.3390/e21030302 ◽

2019 ◽

Vol 21 (3) ◽

pp. 302 ◽

Cited By ~ 4

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.

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On the Roughness of Quasinilpotency Property of One-parameter Semigroups

Canadian Mathematical Bulletin ◽

10.4153/cmb-2016-088-0 ◽

2017 ◽

Vol 60 (2) ◽

pp. 364-371 ◽

Cited By ~ 1

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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The Dynamical Systems Theory Approach to Transport and Mixing in Fluids

Lagrangian Oceanography - Physics of Earth and Space Environments ◽

10.1007/978-3-319-53022-2_1 ◽

2017 ◽

pp. 1-17

Author(s):

Sergey V. Prants ◽

Michael Yu. Uleysky ◽

Maxim V. Budyansky

Keyword(s):

Dynamical Systems ◽

Systems Theory ◽

Dynamical Systems Theory ◽

Theory Approach ◽

Transport And Mixing

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Information processing and dynamical systems approaches are complementary

Behavioral and Brain Sciences ◽

10.1017/s0140525x02430117 ◽

2002 ◽

Vol 25 (5) ◽

pp. 639-640

Author(s):

David Spurrett

Keyword(s):

Information Processing ◽

Dynamical Systems ◽

Systems Theory ◽

Dynamical Systems Theory ◽

Communication Studies ◽

New Paradigm ◽

Systems Approaches ◽

False Dichotomy ◽

Language Research ◽

Ape Language

Shanker & King (S&K) trumpet the adoption of a “new paradigm” in communication studies, exemplified by ape language research. Though cautiously sympathetic, I maintain that their argument relies on a false dichotomy between “information” and “dynamical systems” theory, and that the resulting confusion prevents them from recognizing the main chance their line of thinking suggests.

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