Dynamics of Boolean Networks
نویسنده
چکیده
Boolean networks are special types of finite state timediscrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in studying these dynamical systems is to link their long term behaviors to the structures of the functions that define them. In this paper, a method for deriving a Boolean network’s dynamical information via its disjunctive normal form is explained. For a given Boolean network, a matrix with entries 0 and 1 is associated with the polynomial function that represents the network, then the information on the fixed points and the limit cycles is derived by analyzing the matrix. The described method provides an algorithm for the determination of the fixed points from the polynomial expression of a Boolean network. The method can also be used to construct Boolean networks with prescribed limit cycles and fixed points. Examples are provided to explain the algorithm.
منابع مشابه
Dynamics of Boolean Networks
Networks are used to model systems consisting of many interacting units. The topology of networks has been studied extensively while there are still many open questions concerning the dynamics of and on networks. Boolean networks refer to a class of dynamics on networks; it is the simplest possible dynamics which allows for analytical studies and easy computer implementation. Applications of ne...
متن کاملSymmetry in critical random Boolean network dynamics.
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at ...
متن کاملDynamics of complex autonomous Boolean networks
Springer-Verlag Gmbh Feb 2015, 2015. Buch. Book Condition: Neu. 244x161x20 mm. Neuware This thesis focuses on the dynamics of autonomous Boolean networks, on the basis of Boolean logic functions in continuous time without external clocking. These networks are realized with integrated circuits on an electronic chip as a field programmable gate array (FPGA) with roughly 100,000 logic gates, offer...
متن کاملBoolean dynamics of biological networks with multiple coupled feedback loops.
Boolean networks have been frequently used to study the dynamics of biological networks. In particular, there have been various studies showing that the network connectivity and the update rule of logical functions affect the dynamics of Boolean networks. There has been, however, relatively little attention paid to the dynamical role of a feedback loop, which is a circular chain of interactions...
متن کاملRealization of Boolean control networks
Based on the linear expression of the dynamics of Boolean networks, the coordinate transformation of Boolean variables is defined. It follows that the state space coordinate transformation for the dynamics of Boolean networks is revealed. Using it, the invariant subspace for a Boolean control network is defined. Then the structure of a Boolean control network is analyzed, and the controllable a...
متن کاملAn Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks
We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of ω-automata, and then t...
متن کامل