An extension of a combinatorial fixed point theorem of Shih and Dong

DOI10.1016/j.aam.2007.05.006zbMath1185.05027OpenAlexW2061168403MaRDI QIDQ953907

Adrien Richard

Publication date: 6 November 2008

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2007.05.006

zbMATH Keywords

fixed pointdiscrete dynamical systemsJacobian conjecturegenetic regulatory networksdiscrete Jacobian matrixBoolean eigenvalueasynchronous automata networks

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Combinatorics in computer science (68R05) Topological dynamics (37B99) Jacobian problem (14R15) Cellular automata (computational aspects) (68Q80) Boolean functions (06E30) Genetics and population dynamics (92D99)

Related Items (10)

Complexity of fixed point counting problems in Boolean networks ⋮ From kernels in directed graphs to fixed points and negative cycles in Boolean networks ⋮ Positive and negative cycles in Boolean networks ⋮ Local Negative Circuits and Cyclic Attractors in Boolean Networks with at most Five Components ⋮ On the conversion of multivalued to Boolean dynamics ⋮ Static Analysis of Boolean Networks Based on Interaction Graphs: A Survey ⋮ Negative circuits and sustained oscillations in asynchronous automata networks ⋮ Local negative circuits and fixed points in non-expansive Boolean networks ⋮ Nilpotent dynamics on signed interaction graphs and weak converses of Thomas' rules ⋮ AN APPLICATION OF A DISCRETE FIXED POINT THEOREM TO A GAME IN EXPANSIVE FORM

Cites Work

• Dérivée discrete et comportement local d'une itération discrete
• Théoremes de Perron-Frobenius et Stein-Rosenberg booleens
• Solution of the Boolean Markus-Yamabe problem
• A combinatorial analogue of the Jacobian problem in automata networks
• Discrete dynamical systems
• Necessary conditions for multistationarity in discrete dynamical systems
• Multistationarity, the basis of cell differentiation and memory. II. Logical analysis of regulatory networks in terms of feedback circuits
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