混沌动力学
Avoided level crossings, commonly associated with quantum chaos, are typically interpreted as signatures of eigenstate hybridization and spatial delocalization, often viewed as ergodic spreading. We show that, contrary to this expectation,…
We investigate the classical dynamics of optical nonlinear Kerr couplers, focusing on their potential relevance to quantum computing applications. The system consists of three Kerr-type nonlinear oscillators arranged in two configurations:…
The standard logistic map, $x'=ax(1-x)$, serves as a paradigmatic model to demonstrate how apparently simple non-linear equations lead to complex and chaotic dynamics. In this work we introduce and investigate its matrix analogue defined…
Eulerian nonlinear uncertainty propagation methods often suffer from finite domain limitations and computational inefficiencies. A recent approach to this class of algorithm, Grid-based Bayesian Estimation Exploiting Sparsity, addresses the…
We investigate the nature of the modifications in the temporal dynamics manifested in the high-frequency EEG spectra of the normal human brain in comparison to the diseased brain undergoing epilepsy. For this purpose, the Fourier…
We bring together three key amplification mechanisms in linear dynamical systems: spectral criticality, resonance, and non-normality. We present a unified linear framework that both distinguishes and quantitatively links these effects…
We investigate symmetry breaking in a time-dependent billiard that undergoes a continuous phase transition when dissipation is introduced. The system presents unlimited velocity, and thus energy growth for the conservative dynamics. When…
A very few three-dimensional (3D) periodic orbits of general three-body problem (with three finite masses) have been discovered since Newton mentioned it in 1680s. Using a high-accuracy numerical strategy we discovered 10,059…
Cluster synchronization in multilayer networks of phase oscillators with phase-lag poses significant challenges due to the destabilizing effects of delayed interactions. Leveraging the Sakaguchi-Kuramoto model, this study addresses these…
This paper explores chaos control in the Sprott circuit by leveraging Stochastic Gradient Descent (SGD) to calibrate Pyragas delayed feedback control. Using a third-order nonlinear differential equation, we model the circuit and aim to…
Templexes are topological objects that encode the branching organization of a flow in phase space. We build on these objects to introduce the concept of topological modes of variability (TMVs). TMVs are defined as dynamical manifestations…
The adiabatic gauge potential (AGP) is the generator of unitary transformations which preserve the eigenbasis of a quantum Hamiltonian under parametric variation. While its usefulness in quantum mechanics has been thoroughly demonstrated in…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
Many studies on acoustic radiation forces focus on characterizing the behavior of acoustic fields. However, the dynamic response of objects, particularly those larger than the wavelength, remains underexplored. Here we bridge this gap by…
We adapt ideas from geometrical optics and classical billiard dynamics to consider particle trajectories with constant velocity on a cone with specular reflections off an elliptical boundary formed by the intersection with a tilted plane,…
Quantum billiards are a key focus in quantum mechanics, offering a simple yet powerful model to study complex quantum features. While the development of algebras for quantum systems is traced from one-dimensional integrable models to…
Coupled Tchebyscheff maps have recently been introduced to explain parameters in the standard model of particle physics, using the stochastic quantisation of Parisi and Wu. This paper studies dynamical properties of these maps, finding…
Since 2011, rafts of floating \emph{Sargassum} seaweed have frequently obstructed the coasts of the Intra-Americas Seas. The motion of the rafts is represented by a high-dimensional nonlinear dynamical system. Referred to as the eBOMB…
Research in multistable systems is a flourishing field with countless examples and applications across scientific disciplines. I present a catalog of multistable dynamical systems covering relevant fields of knowledge. This work is focused…
In previous studies, the propagation of extreme events across nodes in monolayer networks has been extensively studied. In this work, we extend this investigation to explore the propagation of extreme events between two distinct layers in a…