Coupled Maps with Growth and Death: An Approach to Cell Differentiation

Abstract

An extension of coupled maps is given which allows for the growth of the number of elements, and is inspired by the cell differentiation problem. The growth of elements is made possible first by clustering the phases, and then by differentiating roles. The former leads to the time sharing of resources, while the latter leads to the separation of roles for the growth. The mechanism of the differentiation of elements is studied. An extension to a model with several internal phase variables is given, which shows differentiation of internal states. The relevance of interacting dynamics with internal states (``intra-inter" dynamics) to biological problems is discussed with an emphasis on heterogeneity by clustering, macroscopic robustness by partial synchronization and recursivity with the selection of initial conditions and digitalization.

LatexText,figures are not included. submitted to PhysicaD (1995,revised 1996 May)

References in corpus (3)

• Relevance of Dynamic Clustering to Biological Networks
• Cell Division, Differentiation and Dynamic Clustering
• Remarks on the mean field dynamics of networks of chaotic elements

Cited by in corpus (3)

• On the Strength of Attractors in a High-dimensional System: Milnor Attractor Network, Robust Global Attraction, and Noise-induced Selection
• Symbiotic Sympatric Speciation: Compliance with Interaction-driven Phenotype Differentiation from a Single Genotype
• Robust and Irreversible Development in Cell Society as a General Consequence of Intra-Inter Dynamics