Related papers: Dynamics in parallel of double Boolean automata ci…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
We introduce a numerical method to study random Boolean networks with asynchronous stochas- tic update. Each node in the network of states starts with equal occupation probability and this probability distribution then evolves to a steady…
We examine the effects of symmetry--preserving and breaking interactions in a drive--response system where the response has an invariant symmetry in the absence of the drive. Subsequent to the onset of generalized synchronization, we find…
This review explains in a self-contained way the properties of random Boolean networks and their attractors, with a special focus on critical networks. Using small example networks, analytical calculations, phenomenological arguments, and…
In dynamical systems on networks, one assigns the dynamics to nodes, which are then coupled via links. This approach does not account for group interactions and dynamics on links and other higher dimensional structures. Higher-order network…
Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…
In the context of discrete dynamical systems and their applications, fixed points often have a clear interpretation. This is indeed a central topic of gene regulatory mechanisms modeled by Boolean automata networks (BANs), where a…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
Given a Boolean network BN and a subset A of attractors of BN, we study the problem of identifying a minimal subset C of vertices of BN, such that the dynamics of BN can reach from a state s in any attractor As in A to any attractor At in A…
The random map model is a deterministic dynamical system in a finite phase space with n points. The map that establishes the dynamics of the system is constructed by randomly choosing, for every point, another one as being its image. We…
We study the class of cooperative Boolean networks whose only regulatory functions are COPY, binary AND, and binary OR. We prove that for all sufficiently large N and c < 2 there exist Boolean networks in this class that have an attractor…
We consider a boolean network whose interaction graph has no circuit of length >1. Under this hypothesis, we establish an upper bound on the length of the attractors of the network which only depends on its interaction graph.
In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or…
We introduce a distributed control architecture for a class of heterogeneous, nonlinear dynamical agents moving in the "string" formation, while guaranteeing trajectory tracking, collision avoidance and the preservation of the formation's…
This paper studies a control method for switching stable coexisting attractors of a class of non-autonomous dynamical systems. The central idea is to introduce a continuous path for the system's trajectory to transition from its original…
Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
We state an algorithm that, given an automata network and a block-sequential update schedule, produces an automata network of the same size or smaller with the same limit dynamics under the parallel update schedule. Then, we focus on the…
We study the target control problem of asynchronous Boolean networks, to identify a set of nodes, the perturbation of which can drive the dynamics of the network from any initial state to the desired steady state (or attractor). We are…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…