CHAOTIC MEAN FIELD DYNAMICS OF A BOOLEAN NETWORK WITH RANDOM CONNECTIVITY

Author:

JOY MALIACKAL POULO1,INGBER DONALD E.1,HUANG SUI1

Affiliation:

1. Vascular Biology Program, Children's Hospital and Harvard Medical School, 300 Longwood Ave, Boston, MA 02115, USA

Abstract

Random Boolean networks have been used as simple models of gene regulatory networks, enabling the study of the dynamic behavior of complex biological systems. However, analytical treatment has been difficult because of the structural heterogeneity and the vast state space of these networks. Here we used mean field approximations to analyze the dynamics of a class of Boolean networks in which nodes have random degree (connectivity) distributions, characterized by the mean degree k and variance D. To achieve this we generalized the simple cellular automata rule 126 and used it as the Boolean function for all nodes. The equation for the evolution of the density of the network state is presented as a one-dimensional map for various input degree distributions, with k and D as the control parameters. The mean field dynamics is compared with the data obtained from the simulations of the Boolean network. Bifurcation diagrams and Lyapunov exponents for different parameter values were computed for the map, showing period doubling route to chaos with increasing k. Onset of chaos was delayed (occurred at higher k) with the increase in variance D of the connectivity. Thus, the network tends to be less chaotic when the heterogeneity, as measured by the variance of connectivity, was higher.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computational Theory and Mathematics,Computer Science Applications,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Influence maximization in Boolean networks;Nature Communications;2022-06-16

2. CHAOS SYNCHRONIZATION IN THE PRESENCE OF NOISE;International Journal of Modern Physics C;2011-12

3. CONTROLLING CHAOS VIA STATE FEEDBACK CANCELLATION IN A NOISY CHAOTIC SYSTEM;International Journal of Modern Physics C;2008-10

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