# Dynamical complexity of discrete-time regulatory networks

@article{Lima2005DynamicalCO, title={Dynamical complexity of discrete-time regulatory networks}, author={Ricardo Lima and Edgardo Ugalde}, journal={Nonlinearity}, year={2005}, volume={19}, pages={237 - 259} }

Genetic regulatory networks are usually modelled by systems of coupled differential equations, and more particularly by systems of piecewise affine differential equations. Finite state models, better known as logical networks, are also used. In this paper we present a class of models of regulatory networks which may be situated in the middle of the spectrum; they present both discrete and continuous aspects. They consist of a network of units, whose states are quantified by a continuous real…

## 31 Citations

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Mathematics

Journal of mathematical biology

Simple models of genetic regulatory networks generated by piecewise affine contracting mappings whose variables represent gene expression levels are introduced and the mathematical analysis of their dynamics is presented.

### Modular Gene Dynamics and Network Theory at Mesoscopic Scale

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Physics

This Thesis studies two-dimensional chaotic maps coupled through non-directed networks with different topologies and examines the dynamical relationship between these two network structures, examining the emergence of cooperativity on a large scale (trees) as a consequence of mesoscale dynamical patterns exhibited by the 4-star.

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Computer Science

We study the dynamical properties of small regulatory networks treated as non autonomous dynamical systems called modules when working inside larger networks or, equivalently when subject to external…

### Robust stability analysis for discrete-time genetic regulatory networks with probabilistic time delays

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Mathematics

Neurocomputing

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Physics

Chaos

This work investigates the collective motion of Chirikov standard maps interacting with time delay through directed links of gene regulatory network of bacterium Escherichia coli and exhibits statistically robust self-organized dynamics in a weakly chaotic regime.

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Mathematics

We study a wide class of dynamical systems defined by the iteration of piecewise contracting maps on compact and locally connected metric spaces. We consider non–isolated discontinuities and finitely…

### Robust state estimation for discrete-time genetic regulatory network with random delays

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Mathematics, Engineering

Neurocomputing

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Mathematics, Computer Science

It is shown that, in a random regulatory network, initial conditions almost certainly converge to a periodic attractor, and it is proved that those modules are dynamically equivalent to independent regulatory networks.

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