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Root selection and dynamical systems

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0007
Subject:
Mathematics, Probability / Statistics

This chapter explores the relationship between the numerical methods described in earlier chapters and the theory of dynamical systems. An estimating function defines a dynamical estimating system, ... More


A Primer for Dynamical Systems

Kevin S. McCann

in Food Webs (MPB-50)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691134178
eISBN:
9781400840687
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691134178.003.0002
Subject:
Biology, Ecology

This chapter introduces the reader to some of the main conceptual ideas behind dynamical systems theory from the perspective of an experimentalist. It first considers the qualitative approaches used ... More


From Causal Reductionism to Self‐Directed Systems

Nancey Murphy and Warren S. Brown

in Did My Neurons Make Me Do It?: Philosophical and Neurobiological Perspectives on Moral Responsibility and Free Will

Published in print:
2007
Published Online:
September 2007
ISBN:
9780199215393
eISBN:
9780191707025
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199215393.003.0003
Subject:
Philosophy, Philosophy of Mind

This chapter criticizes overly-simple accounts of causal processes, particularly atomist-reductionism-determinism. Alternatively, a case is made for considering downward causation (the effect of the ... More


Isochronous Systems

Francesco Calogero

Published in print:
2008
Published Online:
May 2008
ISBN:
9780199535286
eISBN:
9780191715853
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535286.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A classical dynamical system is called isochronous if it features in its phase space an open, fully dimensional sector where all its solutions are periodic in all their degrees of freedom with the ... More


Development as Change of System Dynamics: Stability, Instability, and Emergence

Gregor Schöner

in Toward a Unified Theory of Development Connectionism and Dynamic System Theory Re-Consider

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195300598
eISBN:
9780199867165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300598.003.0002
Subject:
Psychology, Cognitive Psychology, Developmental Psychology

Dynamical systems thinking can provide metaphors that help ask new questions, generate new experimental paradigms and measures, and lead to new kinds of explanations. This chapter reviews dynamical ... More


Dynamical Systems Theory

Robert D. Rupert

in Cognitive Systems and the Extended Mind

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195379457
eISBN:
9780199869114
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195379457.003.0007
Subject:
Philosophy, Philosophy of Mind

This chapter addresses a long-running theme in the literature on extended cognition: the dynamical coupling of the organism and the environment. Six kinds of dynamical-systems-based model are ... More


Numerical Methods for Nonlinear Estimating Equations

Christopher G. Small and Jinfang Wang

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.001.0001
Subject:
Mathematics, Probability / Statistics

Nonlinearity arises in statistical inference in various ways, with varying degrees of severity, as an obstacle to statistical analysis. More entrenched forms of nonlinearity often require intensive ... More


Connectionist Models of Development: Mechanistic Dynamical Models with Emergent Dynamical Properties

James L. McClelland and Gautam Vallabha

in Toward a Unified Theory of Development Connectionism and Dynamic System Theory Re-Consider

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195300598
eISBN:
9780199867165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300598.003.0001
Subject:
Psychology, Cognitive Psychology, Developmental Psychology

This chapter attempts to underscore the common ground between connectionist and dynamical systems approaches. Central to both approaches is the emergent nature of system-level behavior and changes to ... More


Toward a Continuity Psychology

Michael Spivey

in The Continuity of Mind

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195170788
eISBN:
9780199786831
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195170788.003.0001
Subject:
Psychology, Cognitive Neuroscience

This chapter outlines the goals of the book: to bring together dynamical systems theory, cognitive and computational neuroscience, connectionism, and ecological psychology to provide an understanding ... More


Analysis of Dynamic Behavior

Domitilla Del Vecchio and Richard M. Murray

in Biomolecular Feedback Systems

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161532
eISBN:
9781400850501
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161532.003.0003
Subject:
Biology, Biochemistry / Molecular Biology

This chapter turns to some of the tools from dynamical systems and feedback control theory that will be used in the rest of the text to analyze and design biological circuits. It first models the ... More


Some Simulation Tools for Tracking Continuous Mental Trajectories

Michael Spivey

in The Continuity of Mind

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195170788
eISBN:
9780199786831
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195170788.003.0004
Subject:
Psychology, Cognitive Neuroscience

This chapter promotes quantitative simulation as an important accompaniment to theoretical and experimental methods in dynamical approaches to understanding the mind. A mathematical introduction is ... More


Dynamical systems on networks: A discussion of dynamical systems on networks, a subject area that is in its infancy but about which we nonetheless have some interesting results

M. E. J. Newman

in Networks: An Introduction

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199206650
eISBN:
9780191594175
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199206650.003.0018
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Many real-world processes — or simplified models of real-world processes — can be represented as dynamical systems on networks. The spread of news or information between friends, the movement of ... More


Transitions in Cognitive Development: Prospects and Limitations of a Neural Dynamic Approach

Han L. J. van der Maas and Maartje E. J. Raijmakers

in Toward a Unified Theory of Development Connectionism and Dynamic System Theory Re-Consider

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195300598
eISBN:
9780199867165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300598.003.0015
Subject:
Psychology, Cognitive Psychology, Developmental Psychology

This chapter discusses old-fashioned cognitive development from the point of view of two modern approaches, connectionism and nonlinear dynamical systems theory. The main assertion in both ... More


Introductory Concepts

Domitilla Del Vecchio and Richard M. Murray

in Biomolecular Feedback Systems

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161532
eISBN:
9781400850501
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161532.003.0001
Subject:
Biology, Biochemistry / Molecular Biology

This chapter provides a brief introduction to concepts from systems biology; tools from differential equations and control theory; and approaches to the modeling, analysis, and design of biomolecular ... More


Some Conceptual Tools for Tracking Continuous Mental Trajectories

Michael Spivey

in The Continuity of Mind

Published in print:
2006
Published Online:
September 2007
ISBN:
9780195170788
eISBN:
9780199786831
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195170788.003.0002
Subject:
Psychology, Cognitive Neuroscience

This chapter introduces the distinction between a pure mental state, which is an idealized (prototype) location in the state space that is never perfectly visited, and a probabilistic mental state, ... More


Quantum Dynamical Systems

Robert Alicki and Mark Fannes

Published in print:
2001
Published Online:
February 2010
ISBN:
9780198504009
eISBN:
9780191708503
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504009.001.0001
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This book presents a number of basic concepts and mathematical techniques for analyzing quantum and classical dynamical systems on an equal basis, mainly but not solely aimed at quantifying ... More


GROUP ORBITALLY CONSTRAINED APPROXIMATION

Moody T. Chu and Gene H. Golub

in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566649
eISBN:
9780191718021
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566649.003.0009
Subject:
Mathematics, Applied Mathematics

Group actions together with properly formulated objective functions can offer a channel to tackle various classical or new and challenging problems rising from applied linear algebra. This chapter ... More


Hybrid Dynamical Systems: Modeling, Stability, and Robustness

Rafal Goebel, Ricardo G. Sanfelice, and Andrew R. Teel

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153896
eISBN:
9781400842636
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153896.001.0001
Subject:
Mathematics, Applied Mathematics

Hybrid dynamical systems exhibit continuous and instantaneous changes, having features of continuous-time and discrete-time dynamical systems. Filled with a wealth of examples to illustrate concepts, ... More


Large-Scale Impulsive Dynamical Systems

Wassim M. Haddad and Sergey G. Nersesov

in Stability and Control of Large-Scale Dynamical Systems: A Vector Dissipative Systems Approach

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153469
eISBN:
9781400842667
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153469.003.0010
Subject:
Mathematics, Applied Mathematics

This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale ... More


Toward a Unified Theory of Development Connectionism and Dynamic System Theory Re-Consider

John Spencer (ed.)

Published in print:
2009
Published Online:
September 2009
ISBN:
9780195300598
eISBN:
9780199867165
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195300598.001.0001
Subject:
Psychology, Cognitive Psychology, Developmental Psychology

From William James to Sigmund Freud to Jean Piaget to B. F. Skinner, scholars (and parents) have wondered how children move from the blooming, buzzing confusion of infancy, through the tumult of ... More


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