Graphic Requirements for Multiple Attractive Cycles in Boolean Dynamical Systems

Authors

  • Jian-Lang Dong Department of Information Management, Shu-Te University, No. 59, Hun Shan Road, Yen Chau, Kaohsiung County, 82445 Taiwan

DOI:

https://doi.org/10.26713/jims.v3i1.38

Keywords:

Gene network, Boolean network, Thomas' conjecture, Fixed point, Attractive cycle, Positive circuit, Interaction graph, Multistationarity, Boolean Jacobian matrix

Abstract

E. Remy, P. Ruet and D. Thieffry have proved a Boolean version of Thomas' conjecture: if a map $F$ from $\{0,1\}^{n}$ to itself has several fixed points, then there exists a positive circuit in the corresponding interaction graph. In this paper, we prove that the presence of a positive circuit in a local interaction graph is also a necessary condition for the presence of several attractive cycles in the Boolean synchronous dynamics.

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Issue

Vol. 3 No. 1 (2011)

Section

Research Article

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How to Cite

Graphic Requirements for Multiple Attractive Cycles in Boolean Dynamical Systems. (2011). Journal of Informatics and Mathematical Sciences, 3(1), 11-29. https://doi.org/10.26713/jims.v3i1.38