Related papers: The Extended Alpha Group Dynamic Mapping
A periodic perturbation such as a laser field cannot induce transitions between two decoupled states for which the transition matrix element vanishes. We show, however, that if in addition some system parameters are varied adiabatically,…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
We study the effects of phase-frustrated, higher-order interactions in a system of coupled phase oscillators with two communities. We use dimensionality reduction techniques to derive a low-dimensional system of ODEs to describe the…
We study the dynamics of phase ordering of a non-conserved, scalar order parameter in one dimension, with long-range interactions characterized by a power law $r^{-d-\sigma}$. In contrast to higher dimensional systems, the point nature of…
We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…
We show that thermodynamics can be formulated naturally from the intrinsic geometry of phase space alone-without postulating an ensemble, which instead emerges from the geometric structure itself. Within this formulation, phase transitions…
Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs)…
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…
Load models have a great impact on voltage behaviors as well as power system transient dynamics. Extensive work has been done on this topic, proposing appropriate load models and capturing better load behaviors during transient. This paper…
I introduce a novel mathematical framework integrating topological dynamics, operator algebras, and ergodic geometry to study lattices of asynchronous metric dynamical systems. Each node in the lattice carries an internal flow represented…
Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…
We derive an elegant solution for a two-level system evolving adiabatically under the influence of a driving field with a time-dependent phase, which includes open system effects such as dephasing and spontaneous emission. This solution,…
Dynamical systems appear in nearly every aspect of the physical world. As such, understanding the properties of dynamical systems is of great importance. Typically, a dynamical system is described by a system of ordinary differential…
Given an autonomous system of ordinary differential equations (ODE), we consider developing practical models for the deterministic, slow/coarse behavior of the ODE system. Two types of coarse variables are considered. The first type…
This paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolutional approach. Approximating the Koopman operator by…
We introduce a combinatorial topological framework for characterizing the global dynamics of ordinary differential equations (ODEs). The approach is motivated by the study of gene regulatory networks, which are often modeled by ODEs that…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…