Equations with fluctuating parameters for an open dynamical system

1979 ◽  
Vol 22 (4) ◽  
pp. 315-317
Author(s):  
G. F. Efremov ◽  
V. A. Kazakov
Keyword(s):  
Dynamical System ◽  
Open Dynamical System

scholarly journals A compositional framework for reaction networks

2017 ◽  
Vol 29 (09) ◽  
pp. 1750028 ◽  
Author(s):  
John C. Baez ◽  
Blake S. Pollard
Keyword(s):  
Dynamical System ◽  
Steady State ◽  
General Framework ◽  
Nonlinear Dynamical System ◽  
Reaction Network ◽  
Reaction Networks ◽  
Nonlinear Dynamical ◽  
Input And Output ◽  
Open Dynamical System ◽  
Steady State Solutions

Reaction networks, or equivalently Petri nets, are a general framework for describing processes in which entities of various kinds interact and turn into other entities. In chemistry, where the reactions are assigned ‘rate constants’, any reaction network gives rise to a nonlinear dynamical system called its ‘rate equation’. Here we generalize these ideas to ‘open’ reaction networks, which allow entities to flow in and out at certain designated inputs and outputs. We treat open reaction networks as morphisms in a category. Composing two such morphisms connects the outputs of the first to the inputs of the second. We construct a functor sending any open reaction network to its corresponding ‘open dynamical system’. This provides a compositional framework for studying the dynamics of reaction networks. We then turn to statics: that is, steady state solutions of open dynamical systems. We construct a ‘black-boxing’ functor that sends any open dynamical system to the relation that it imposes between input and output variables in steady states. This extends our earlier work on black-boxing for Markov processes.

RECURRENT NEURAL NETWORKS ARE UNIVERSAL APPROXIMATORS

2007 ◽  
Vol 17 (04) ◽  
pp. 253-263 ◽  
Author(s):  
ANTON MAXIMILIAN SCHÄFER ◽  
HANS-GEORG ZIMMERMANN
Keyword(s):  
Dynamical System ◽  
Neural Networks ◽  
Dynamical Systems ◽  
Error Correction ◽  
Recurrent Neural Networks ◽  
State Space Model ◽  
Universal Approximation ◽  
Space Model ◽  
Open Dynamical System ◽  
Universal Approximators

Recurrent Neural Networks (RNN) have been developed for a better understanding and analysis of open dynamical systems. Still the question often arises if RNN are able to map every open dynamical system, which would be desirable for a broad spectrum of applications. In this article we give a proof for the universal approximation ability of RNN in state space model form and even extend it to Error Correction and Normalized Recurrent Neural Networks.

scholarly journals The concept of an open dynamic system

2020 ◽  
Vol 3 ◽  
pp. 3-22
Author(s):  
O.M. Reznik ◽  
Keyword(s):  
Dynamical System ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Social Intelligence ◽  
Classical Model ◽  
Space Time ◽  
Internal Space ◽  
Open Dynamical System ◽  
New Interpretation ◽  
Multicellular Organisms

The concept of an open dynamical system as a general model of the development of systems and processes of various nature is proposed. It is based on a new interpretation of M. Mesarovich’s theorem on the decomposition of the Universum, and the concept of observation as an asymmetric relation corresponding to the movement of basis elements of a set of states of a dynamical system between its external and internal space. The element of the basis, according to the concept of geometrodynamics, exists as a vortex in an empty curved internal space of a dynamical system, or as an elementary particle that transfers a quantum of energy when observed. An open dynamical system is defined as a finite dynamical system exchanging observations with the environment, divided into local, representing an inverse dynamical system, and external, where external observations come from. In the intervals between external observations, it exists as a conservative dynamical system. It is regarded the evolution of dynamic systems in the process of expansion and cooling of the Universe: the appearance of elementary particles and atoms, the formation of complex molecules and chain macromolecules, the appearance of living cells, the formation of multicellular organisms, the nervous system and the brain, the appearance of a human and the intellect, the development of society and civilization. With the emergence of life, open dynamic systems became distributed and perform the functions of natural selection of members of the population, and after the appearance of intelligence and the formation of society, they realize social intelligence and become virtual. Threats of uncontrolled behavior of virtual systems, in particular digital artificial intelligence systems, which can neglect the discreteness of space-time due to the use in their design of the classical model of infinitesimal, which do not exist due to the discreteness of space-time, are considered. The incompatibility of the classical model with the discrete model of an open dynamic system is an urgent scientific problem that requires further study.

Network Invasion as an Open Dynamical System: Response to Rossberg and Barabás

2019 ◽  
Vol 34 (5) ◽  
pp. 386-387
Author(s):  
Cang Hui ◽  
David M. Richardson
Keyword(s):  
Dynamical System ◽  
System Response ◽  
Open Dynamical System

Chaos and Creativity: The Psique as a Complex Dynamical System Creativiy and Arquetipal Psychology

2012 ◽  
Author(s):  
Magaly Villaobos ◽  
Yolanda Ng Lee ◽  
Maria Elena Gutierrez
Keyword(s):  
Dynamical System ◽  
Complex Dynamical System

Spontaneous pattern classification by a dynamical system

1987 ◽  
Vol 48 (12) ◽  
pp. 2027-2035 ◽  
Author(s):  
W. Banzhaf
Keyword(s):  
Dynamical System ◽  
Pattern Classification
Sign in / Sign up

Export Citation Format

Share Document