Related papers: Attractor identification in asynchronous Boolean d…
We propose a new method to recover global information about a network of interconnected dynamical systems based on observations made at a small number (possibly one) of its nodes. In contrast to classical identification of full graph…
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…
In abstractions of linear dynamic networks, selected node signals are removed from the network, while keeping the remaining node signals invariant. The topology and link dynamics, or modules, of an abstracted network will generally be…
We propose the use of Deterministic Generalized Asynchronous Random Boolean Networks [Gershenson, 2002] as models of contextual deterministic discrete dynamical systems. We show that changes in the context have drastic effects on the global…
In this work, we explore the state-space formulation of a network process to recover, from partial observations, the underlying network topology that drives its dynamics. To do so, we employ subspace techniques borrowed from system…
We consider the following question on the relationship between the asymptotic behaviours of asynchronous dynamics of Boolean networks and their regulatory structures: does the presence of a cyclic attractor imply the existence of a local…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…
This paper examines the use of operator-theoretic approaches to the analysis of chaotic systems through the lens of their unstable periodic orbits (UPOs). Our approach involves three data-driven steps for detecting, identifying, and…
We introduce an adaptation algorithm by which an ensemble of coupled oscillators with attractive and repulsive interactions is induced to adopt a prescribed synchronized state. While the performance of adaptation is controlled by measuring…
Dynamical systems theory and complexity science provide powerful tools for analysing artificial agents and robots. Furthermore, they have been recently proposed also as a source of design principles and guidelines. Boolean networks are a…
The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict…
Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks,…
Many complex systems in biology, physics, and engineering include a large number of state-variables, and measuring the full state of the system is often impossible. Typically, a set of sensors is used to measure part of the state-variables.…
A replicator equation with mutation processes is numerically studied. Without any mutations, two characteristics of the replicator dynamics are known: an exponential divergence of the dominance period, and hierarchical orderings of the…
We consider Hodgkin-Huxley-type model that is a stiff ODE system with two fast and one slow variables. For the parameter ranges under consideration the original version of the model has unstable fixed point and the oscillating attractor…
The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is first proved that the trajectory field of the stochastic delayed…
Different Boolean networks may reveal similar dynamics although their definition differs, then preventing their distinction from the observations. This raises the question about the sufficiency of a particular Boolean network for properly…
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…