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The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in both directions. The objective of this paper is to explore a…
The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i)…
Fluctuation theorems (FTs) quantify the thermodynamic reversibility of a system, and for deterministic systems they are defined in terms of the dissipation function. However, in a nonequilibrium steady state of deterministic dynamics, the…
An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to…
Control Barrier Functions (CBFs) offer a framework for ensuring set invariance and designing constrained control laws. However, crafting a valid CBF relies on system-specific assumptions and the availability of an accurate system model,…
Symbolic dynamics has proven to be an invaluable tool in analyzing the mechanisms that lead to unpredictability and random behavior in nonlinear dynamical systems. Surprisingly, a discrete partition of continuous state space can produce a…
We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead…
We will show the central limit theorem for the general one-dimensional lattice where the space of symbols is a compact metric space. We consider the CLT for Lipschitz-Gibbs probabilities and in the proof we use several properties of the…
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective.…
We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…
In an intelligent transportation system, the key problem of traffic forecasting is how to extract periodic temporal dependencies and complex spatial correlations. Current state-of-the-art methods for predicting traffic flow are based on…
Subdiffusion on graphs is often modeled by time-fractional diffusion equations, yet its structural and dynamical consequences remain unclear. We show that subdiffusive transport on graphs is a memory-driven process generated by a random…
Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…
Central moment lattice Boltzmann method (LBM) is one of the more recent developments among the lattice kinetic schemes for computational fluid dynamics. A key element in this approach is the use of central moments to specify collision…
Traffic prediction in data-scarce, cross-city settings is challenging due to complex nonlinear dynamics and domain shifts. Existing methods often fail to capture traffic's inherent chaotic nature for effective few-shot learning. We propose…
We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the…
A broad class of systems, including ecological, epidemiological, and sociological ones, are characterized by populations of individuals assigned to specific categories, e.g., a chemical species, an opinion or an epidemic state, that are…
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
The vibrational predissociation of the Ne2Br2(B) van der Waals complex has been investigated using the quasi-classical trajectory method (QCT), in the range of vibrational levels v' = 16-23. Extensive comparison is made with the most recent…