Related papers: Universality in Globally Coupled Maps and Flows
Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such…
We investigate the relationship between the emergence of chaos synchronization and the information flow in dynamical systems possessing homogeneous or heterogeneous global interactions whose origin can be external (driven systems) or…
Synchronization, the temporal coordination of coupled oscillators, allows fireflies to flash in unison, neurons to fire collectively and human crowds to fall in step on the London Millenium bridge. Here, we interpret active (or…
We characterize universal features of the sample-to-sample fluctuations of global geometrical observables, such as the area, width, length, and center-of-mass position, in random growing planar clusters. Our examples are taken from…
We investigate generalized phase transitions of type localization - delocalization from one to several Sinai-Bowen-Ruelle invariant measures in finite networks of chaotic elements (coupled map lattices) with general graphs of connections in…
Graph convolutional networks (GCNs) are \emph{discriminative models} that directly model the class posterior $p(y|\mathbf{x})$ for semi-supervised classification of graph data. While being effective, as a representation learning approach,…
Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social…
A symmetry breaking mechanism is shown to occur in an array composed of symmetric bistable Lorenz units coupled through a nearest neighbour scheme. When the coupling is increased, we observe the route: standing --> oscillating -->…
A system of N unidimensional global coupled maps (GCM), which support multiattractors is studied. We analize the phase diagram and some special features of the transitions (volume ratios and characteristic exponents), by controlling the…
Graph Neural Networks (GNNs) are powerful learning methods for recommender systems owing to their robustness in handling complicated user-item interactions. Recently, the integration of contrastive learning with GNNs has demonstrated…
We consider a system of two identical linearly coupled Lorenz oscillators, presenting synchro- nization of chaotic motion for a specified range of the coupling strength. We verify the existence of global synchronization and…
We study the dynamics of an ensemble of globally coupled chaotic logistic maps under the action of a learning algorithm aimed at driving the system from incoherent collective evolution to a state of spontaneous full synchronization.…
The peculiar phase-ordering properties of a lattice of coupled chaotic maps studied recently (A. Lema\^\i tre & H. Chat\'e, {\em Phys. Rev. Lett.} {\bf 82}, 1140 (1999)) are revisited with the help of detailed investigations of interface…
We study a synchronization mechanism, based on one-way coupling of all-or-nothing type, applied to coupled map lattices with several different local rules. By analyzing the metric and the topological distance between the two systems, we…
Near a continuous phase transition, systems with different microscopic origins display universal dynamics if their underlying symmetries are compatible. In a thermally quenched system, the Kibble-Zurek mechanism for the creation of…
In lattice gauge theory, there exist field transformations that map the theory to the trivial one, where the basic field variables are completely decoupled from one another. Such maps can be constructed systematically by integrating certain…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.
We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a…
The number of clusters per site $n(p)$ in percolation at the critical point $p = p_c$ is not itself a universal quantity---it depends upon the lattice and percolation type (site or bond). However, many of its properties, including…