Related papers: Chaos in a continuous-time Boolean network
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
We study the versatile performance of networks of coupled circuits. Each of these circuits is composed of a positive and a negative feedback loop in a motif that is frequently found in genetic and neural networks. When two of these circuits…
We formulate general rules for a coarse-graining of the dynamics, which we term `symbolic dynamics', of feedback networks with monotone interactions, such as most biological modules. Networks which are more complex than simple cyclic…
Spiral waves are investigated in chemical systems whose underlying spatially-homogeneous dynamics is governed by a deterministic chaotic attractor. We show how the local periodic behavior in the vicinity of a spiral defect is transformed to…
A model of Boolean agents competing in a market is presented where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long…
This paper aims at setting the keystone of a prospective theoretical study on the role of non-monotone interactions in biological regulation networks. Focusing on discrete models of these networks, namely, Boolean automata networks, we…
We report on a new type of chimera state that attracts almost all initial conditions and exhibits power-law switching behavior in networks of coupled oscillators. Such switching chimeras consist of two symmetric configurations, which we…
We study experimentally the synchronization patterns in time-delayed directed Boolean networks of excitable systems. We observe a transition in the network dynamics when the refractory time of the individual systems is adjusted. When the…
What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…
We study the evolution of the dynamics across a generic first order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis…
We study the dynamics of a bouncing coin whose motion is restricted to the two-dimensional plane. Such coin model is equivalent to the system of two equal masses connected by a rigid rod, making elastic collisions with a flat boundary. We…
The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility…
Information in a chaotic quantum system will scramble across the system, preventing any local measurement from reconstructing it. The scrambling dynamics is key to understanding a wide range of quantum many-body systems. Here we use Holevo…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
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 order to analyze the effect of chaos or order on the rate of decoherence in a subsystem we aim to distinguish effects of the two types of dynamics from those depending on the choice of the wave packet. To isolate the former we introduce…
We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the…
Oscillatory activities are widely observed in specific frequency bands of recorded field potentials in different brain regions, and play critical roles in processing neural information. Understanding the structure of these oscillatory…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…