Function dynamics

Takahashi, Yasuo; Kataoka, Naoto; Kaneko, Kunihiko; Namiki, Takao

doi:10.1007/bf03168583

Cited by 4 publications

(4 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As stated in a previous paper [17], the dynamics of a description can be formulated using a certain type of functional map (see also Refs. [8], [15], [16]). The use of such a map may provide a direction for the development of the present framework.…”

Section: Discussionmentioning

confidence: 99%

Internal logic viewed from observation space: Theory and a case study

Hatakeyama

Tsuda

2007

Biosystems

View full text Add to dashboard Cite

We propose a framework of neurocognitive experiments that clarifies the mathematical structure of experiments and can be used to analyze experimental results and to determine the limitation of their possible interpretation. In contrast to the conventional analysis that employs simple Boolean logic, the present analysis treats classification in terms of higher-order functions. We also predict the existence of a previously unidentified type of neuron.

show abstract

Section: Discussionmentioning

confidence: 99%

Internal logic viewed from observation space: Theory and a case study

Hatakeyama

Tsuda

2007

Biosystems

View full text Add to dashboard Cite

show abstract

“…Takahashi and Namiki, who proved the existence of a hierarchical structure of periodic solutions. [39][40][41] In the Kataoka-Kaneko formula, the presence of the self-referential term of description in Eq. 22 The stability of dynamical systems associated with descriptions can be defined in a similar way.…”

Section: Description Dynamics For External Phenomenamentioning

confidence: 99%

Logic Dynamics for Deductive Inference — Its Stability and Neural Basis

Tsuda¹

2014

Chaos, Information Processing and Paradoxical Games

View full text Add to dashboard Cite

We propose a dynamical model that represents a process of deductive inference. We discuss the stability of logic dynamics and a neural basis for the dynamics. We propose a new concept of descriptive stability, thereby enabling a structure of stable descriptions of mathematical models concerning dynamic phenomena to be clarified. The present theory is based on the wider and deeper thoughts of John S. Nicolis. In particular, it is based on our joint paper on the chaos theory of human short-term memories with a magic number of seven plus or minus two.

show abstract

“…We investigated the FD using a 'generated map' in earlier papers [2] [3]. This generated map is defined as…”

Section: Generated Mapmentioning

confidence: 99%

“…To serve the present purpose of studying biological systems, The function dynamics (FD) that we previously introduced [1][2] [3] is reformulated in Sec.2. In this FD, we adopt a functional equation having a 'self-reference' term, i.e., a term including composition of a function (say f • f ).…”

Section: Introductionmentioning

confidence: 99%

Dynamical networks in function dynamics

Kataoka¹,

Kaneko²

2003

Physica D: Nonlinear Phenomena

Self Cite

View full text Add to dashboard Cite

As a first step toward realizing a dynamical system that evolves while spontaneously determining its own rule for time evolution, function dynamics (FD) is analyzed. FD consists of a functional equation with a self-referential term, given as a dynamical system of a 1-dimensional map. Through the time evolution of this system, a dynamical graph (a network) emerges. This graph has three interesting properties: i) vertices appear as stable elements, ii) the terminals of directed edges change in time, and iii) some vertices determine the dynamics of edges, and edges determine the stability of the vertices, complementarily. Two aspects of FD are studied, the generation of a graph (network) structure and the dynamics of this graph (network) in the system.

show abstract

Function dynamics

Abstract: We show mathematical structure of the function dynamics, i.e., the dynamics of interval maps f"+1 = ( 1 -e) ff + e fn o f,, and clarify the types of fixed points, the self-referential structure and the hierarchical structure.

Cited by 4 publications

References 2 publications

Internal logic viewed from observation space: Theory and a case study

Internal logic viewed from observation space: Theory and a case study

Logic Dynamics for Deductive Inference — Its Stability and Neural Basis

Dynamical networks in function dynamics

Contact Info

Product

Resources

About