Related papers: Realization of Arbitrary Hysteresis by a Low-dimen…
Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating…
Hysteresis is observed at second order phase transitions. Universal scaling formul\ae{} for the areas of hysteresis loops are written down. Critical exponents are defined, and related to other exponents for static and dynamic critical…
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a…
For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell…
We demonstrate that scale-free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle-node bifurcation. Remarkably, the scale-free patterns appear only at a particular time in relaxation…
We show that by restricting the degrees of the vertices of a graph to an arbitrary set \( \Delta \), the threshold point $ \alpha(\Delta) $ of the phase transition for a random graph with $ n $ vertices and $ m = \alpha(\Delta) n $ edges…
Gradient-flow analyses show that simplified linear transformers can learn the in-context linear-regression algorithm, but they do not explain the finite-step behavior of gradient descent at large learning rates. Motivated by empirical work…
Hysteresis is treated as a history dependent branching, and the use of the classical Preisach model for the analysis of macroeconomic hysteresis is first discussed. Then, a new Preisach-type model is introduced as a macroeconomic…
We introduce a simple nonequilibrium model for a driven diffusive system with nonconservative reaction kinetics which exhibits ergodicity breaking and hysteresis in one dimension. These phenomena can be understood through a description of…
We describe a numerical study of the potential energy landscape for the two-dimensional XY model (with no disorder), considering up to 100 spins and CPU and GPU implementations of local optimization, focusing on minima and saddles of index…
Automata networks can be seen as bare finite dynamical systems, but their growing theory has shown the importance of the underlying communication graph of such networks. This paper tackles the question of what dynamics can be realized up to…
The $d$-process generates a graph at random by starting with an empty graph with $n$ vertices, then adding edges one at a time uniformly at random among all pairs of vertices which have degrees at most $d-1$ and are not mutually joined. We…
In the past two decades, various properties of randomly perturbed/augmented (hyper)graphs have been intensively studied, since the model was introduced by Bohman, Frieze and Martin in 2003. The model usually considers a deterministic graph…
This paper proposes a conceptual model for the onset of a stable torus near a saddle-focus equilibrium. This bifurcation scenario is typical of slow-fast systems that generate elliptic bursting in a variety of neuronal models in…
Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open…
We give a nontechnical description of the behaviour of dynamical systems governed by two distinct time scales. We discuss in particular memory effects, such as bifurcation delay and hysteresis, and comment the scaling behaviour of…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
It is well-known that the fundamental diagram in a realistic traffic system is featured by capacity drop. From a mesoscopic approach, we demonstrate that such a phenomenon is linked to the unique properties of stochastic noise, which, when…
In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the theoretical framework for the analysis of the saddle-node…
Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…