Related papers: Phase Space Structures of k-threshold Sequential D…
We map the phase-space trajectories of an external-cavity semiconductor laser using phase portraits. This is both a visualization tool as well as a thoroughly quantitative approach enabling unprecedented insight into the dynamical regimes,…
There is a whole range of emergent phenomena in non-equilibrium behaviors can be well described by a set of stochastic differential equations. Inspired by an insight gained during our study of robustness and stability in phage lambda…
In the literature, for semidynamical systems in infinite dimensional phase spaces, different topological structures are used (Hilbert, Banach, Sobolev, locally convex, Hausdorf topology etc.). That is because there are neither set rules nor…
We study the phase space for an scalar-tensor string inspired model of dark energy with non minimal kinetic and Gauss Bonnet couplings. The form of the scalar potential and of the coupling terms is of the exponential type, which give rise…
Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
For two-component assemblies, an inherent structure diagram (ISD) is the relationship between set inter-subunit energies and the types of kinetic traps (inherent structures) one may obtain from those energies. It has recently been shown…
This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from…
Features of synchronization picture in the system with the limit cycle embedded in a three-dimensional phase space are considered. By the example of Ressler system and Dmitriev - Kislov generator under the action of a periodic sequence of…
Despite hundreds of millions of parameters, transformer training trajectories evolve within only a few coherent directions. We introduce Spectral Edge Dynamics (SED) to quantify this structure: a rolling-window SVD of parameter updates…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
We consider the phase space for a system of $n$ identical qudits (each one of dimension $d$, with $d$ a primer number) as a grid of $d^{n} \times d^{n}$ points and use the finite field $GF(d^{n})$ to label the corresponding axes. The…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
We study the dynamics in the neighborhood of fixed points in a 4D symplectic map by means of the color and rotation method. We compare the results with the corresponding cases encountered in galactic type potentials and we find that they…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
We study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…
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…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…