Related papers: Local negative circuits and cyclic attractors in B…
Arithmetic circuits (AC) are circuits over the real numbers with 0/1-valued input variables whose gates compute the sum or the product of their inputs. Positive AC -- that is, AC representing non-negative functions -- subsume many…
The strong cycle double cover conjecture states that for every circuit $C$ of a bridgeless cubic graph $G$, there is a cycle double cover of $G$ which contains $C$. We conjecture that there is even a 5-cycle double cover $S$ of $G$ which…
Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates.…
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…
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…
A long standing problem in the area of error correcting codes asks whether there exist good cyclic codes. Most of the known results point in the direction of a negative answer. The uncertainty principle is a classical result of harmonic…
We study the global synchronization of hierarchically-organized Stuart-Landau oscillators, where each subsystem consists of three oscillators with activity-dependent couplings. We consider all possible coupling signs between the three…
In a coupled network cells can interact in several ways. There is a vast literature from the last twenty years that investigates this interacting dynamics under a graph theory formalism, namely as a graph endowed with an input-equivalence…
Consider two conditions on a graph: (1) each 5-cycle is not a subgraph of 5-wheel and does not share exactly one edge with 3-cycle, and (2) each 5-cycle is not adjacent to two 3-cycles and is not adjacent to a 4-cycle with chord. We show…
Closed-loop positivity of feedback interconnections of positive monotone nonlinear systems is investigated. It is shown that an instantaneous gain condition on the open-loop systems which implies feedback well-posedness also guarantees…
When is it safe to approximate a complicated random Boolean network (RBN) as a simplified, easier to model RBN? When can static measures of network structure be reliably used to infer the network's dynamics? This simple experiment tests the…
We consider unstable attractors; Milnor attractors $A$ such that, for some neighbourhood $U$ of $A$, almost all initial conditions leave $U$. Previous research strongly suggests that unstable attractors exist and even occur robustly (i.e.…
The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in…
Through computer-assisted enumeration, we list minimal obstructions for 5-choosability of graphs on the torus with the following additional property: There exists a cyclic system of non-contractible triangles around the torus where the…
In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit…
Identity, response to external stimuli, and spatial architecture of a living system are central topics of molecular biology. Presently, they are largely seen as a result of the interplay between a gene repertoire and the regulatory…
A recent problem in dynamics is to determinate whether an attractor $\Lambda$ of a $C^r$ flow $X$ is $C^r$ robust transitive or not. By {\em attractor} we mean a transitive set to which all positive orbits close to it converge. An attractor…
Biological systems operate under persistent noise, which can alter system states and induce transitions between attractors. Here, we study the attractor dynamics of Boolean networks focusing on the transitions between attractors induced by…
We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external…
We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for…