相关论文: Data-Driven Modeling of Global Bifurcations and Ch…

Spatio-temporal chaos in parametrically driven waves is investigated in one and two dimensions using numerical simulations of Ginzburg-Landau equations. A regime is identified in which in one dimension the dynamics are due to double phase…

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…

We introduce a data-driven approach to building reduced dynamical models through manifold learning; the reduced latent space is discovered using Diffusion Maps (a manifold learning technique) on time series data. A second round of Diffusion…

We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…

Multi-body mechanical systems have rich internal dynamics, whose solutions can be exploited as efficient control targets. Yet, solutions non-trivially depend on system parameters, obscuring feasible properties for use as target…

The Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as a coupled phase oscillators. In this paper, a bifurcation structure of the infinite dimensional Kuramoto model is…

Short-term traffic forecasting based on deep learning methods, especially long short-term memory (LSTM) neural networks, has received much attention in recent years. However, the potential of deep learning methods in traffic forecasting has…

Delays are ubiquitous in modern hybrid systems, which exhibit both continuous and discrete dynamical behaviors. Induced by signal transmission, conversion, the nature of plants, and so on, delays may appear either in the continuous…

This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…

The novel idea presented in this paper is to interweave distributed model predictive control with a reliable scheduling of the information that is interchanged between local controllers of the plant subsystems. To this end, a dynamic model…

Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…

We present a general theory of stochastic model reduction which is based on a normal form coordinate transform method of A.J. Roberts. This nonlinear, stochastic projection allows for the deterministic and stochastic dynamics to interact…

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…

We study delay-induced transitions in consensus dynamics on signed networks with a ring topology. The proposed model is formulated as a system of delay differential equations incorporating both cooperative and antagonistic interactions, as…

The double pendulum, a simple system of classical mechanics, is widely studied as an example of, and testbed for, chaotic dynamics. In 2016, Maiti et al. studied a generalization of the simple double pendulum with equal point-masses at…

We study the problem of traffic forecasting, aiming to predict the inflow and outflow of a region in the subsequent time slot. The problem is complex due to the intricate spatial and temporal interdependence among regions. Prior works study…

We report on the dynamics of localized structures in an inhomogeneous Swift-Hohenberg model describing pattern formation in the transverse plane of an optical cavity. This real order parameter equation is valid close to the second order…

We consider a possible application of the Wa\.zewski topological method to feedback control systems and to more general dynamical systems. We show how this method can be used to prove the impossibility of global stabilization in such…

We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of…

We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external…