Related papers: Attractor identification in asynchronous Boolean d…
We investigate how elimination of variables can affect the asymptotic dynamics and phenotype control of Boolean networks. In particular, we look at the impact on minimal trap spaces, and identify a structural condition that guarantees their…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
We compare various concepts of attractor in the context of non-autonomous dynamical systems. Then, we prove an appropriate version of the Pliss reduction principle for non-autonomous differential systems with rapidly oscillating…
We present a method to infer network connectivity from collective dynamics in networks of synchronizing phase oscillators. We study the long-term stationary response to temporally constant driving. For a given driving condition, measuring…
Connecting the dynamics of biomolecular networks to experimentally measurable cell phenotypes remains a central challenge in systems biology. Here we introduce a model-based definition of phenotype as a partial steady state that is…
Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For…
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…
A Boolean network is a mapping $f :\{0,1\}^n \to \{0,1\}^n$, which can be used to model networks of $n$ interacting entities, each having a local Boolean state that evolves over time according to a deterministic function of the current…
We investigate the influence of a deterministic but non-synchronous update on Random Boolean Networks, with a focus on critical networks. Knowing that ``relevant components'' determine the number and length of attractors, we focus on such…
We already know a great deal about dynamical systems with uniqueness in forward time. Indeed, flows, semiflows, and maps (both invertible and not) have been studied at length. A view that has proven particularly fruitful is topological:…
Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the…
In a complex system, the interactions between individual agents often lead to emergent collective behavior like spontaneous synchronization, swarming, and pattern formation. The topology of the network of interactions can have a dramatic…
Because the attractors of biological networks reflect stable behaviors (e.g., cell phenotypes), identifying control interventions that can drive a system towards its attractors (attractor control) is of particular relevance when controlling…
We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory…
Despite the large quantity of information available, thorough researches in various biological databases are still needed in order to reconstruct and understand the steps that lead to known or new phenomena. By using protein-protein…
We investigate how classifiers for Boolean networks (BNs) can be constructed and modified under constraints. A typical constraint is to observe only states in attractors or even more specifically steady states of BNs. Steady states of BNs…
This paper introduces a convex optimization framework for identifying switched network systems, in which both the node dynamics and the underlying graph topology switch between a finite number of configurations. Building on our recent…
Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. An important task in such systems is to extract a simplified view of their time-dependent network of interactions.…
Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…