Related papers: Stable and unstable attractors in Boolean networks
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
We study an extended system that without noise shows a spatially homogeneous state, but when submitted to an adequate multiplicative noise, some "noise-induced patterns" arise. The stochastic resonance between these structures is…
We study the dynamical states that emerge in a small-world network of recurrently coupled excitable neurons through both numerical and analytical methods. These dynamics depend in large part on the fraction of long-range connections or…
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…
Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive…
We investigate the nonlinear parity-time (PT) symmetric coupler from a dynamical perspective. As opposed to linear PT-coupler where the PT threshold dictates the evolutionary characteristics of optical power in the two waveguides, in a…
This paper proposes a new methodology for design of a stabilizing control law for multi-input linear systems with time-varying, singular gains on the control. The results presented here assume the control gain to satisfy persistence of…
We study non-supersymmetric attractors obtained in Type IIA compactifications on Calabi Yau manifolds. Determining if an attractor is stable or unstable requires an algebraically complicated analysis in general. We show using group…
Attractors in parity games are a technical device for solving "alternating" reachability of given node sets. A well known solver of parity games - Zielonka's algorithm - uses such attractor computations recursively. We here propose new…
We consider an autonomous system constructed as modification of the logistic differential equation with delay that generates successive trains of oscillations with phases evolving according to chaotic maps. The system contains two feedback…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
We study the response of an attractor neural network, in the ferromagnetic phase, to an external, time-dependent stimulus, which drives the system periodically two different attractors. We demonstrate a non-trivial dependance of the system…
Random boolean cellular automata are investigated, where each gate has two randomly chosen inputs and is randomly assigned a boolean function of its inputs. The effect of non-uniform distributions on the choice of the boolean functions is…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
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…
We present mathematical techniques for exhaustive studies of long-term dynamics of asynchronous biological system models. Specifically, we extend the notion of $\kappa$-equivalence developed for graph dynamical systems to support systematic…
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in…
A noise-reduction algorithm for time-series of non-linear systems is presented. The algorithm smoothes the attractors in phase space using B-splines, allowing a more accurate measure of their dynamics. The algorithm is tested on numerical…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…