Boolean Monomial Dynamical Systems
arXiv:math/0403166 · doi:10.1007/s00026-004-0230-6
Abstract
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can be described by monomials (including Boolean AND systems), one can obtain information about the limit cycle structure from the structure of the monomials. In particular, the paper contains a sufficient condition for a monomial system to have only fixed points as limit cycles. This condition depends on the cycle structure of the dependency graph of the system and can be verified in polynomial time.
13 pages, 1 ps figure
Cited by in corpus (18)
- A mathematical formalism for agent-based modeling
- The Dynamics of Conjunctive and Disjunctive Boolean Networks
- Linear Dynamical Systems over Finite Rings
- Stabilization Bounds for Linear Finite Dynamical Systems
- Asymptotic Behavior of Conjunctive Boolean Networks Over Weakly Connected Digraphs
- Dynamics of Boolean Networks
- Stability Structures of Conjunctive Boolean Networks
- Large attractors in cooperative bi-quadratic Boolean networks. Part II
- An algebraic and graph theoretical framework to study monomial dynamical systems over a finite field
- The Dynamics of Semilattice Networks
- Controllability of Conjunctive Boolean Networks with Application to Gene Regulation
- Monomial Dynamical Systems over Finite Fields
- Boolean Networks with Multi-Expressions and Parameters
- Characterization of Boolean Networks with Single or Bistable States
- Dynamical properties of disjunctive Boolean networks
- Monomial Dynamical Systems of Dimension One over Finite Fields
- An Algorithm for Detecting Fixed Points of Boolean Networks
- Perspectives and Networks