Related papers: Dynamical System Analysis for Steep Potentials
Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…
Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one dimensional implicitly defined discrete dynamical systems. The backward…
We modify the symmetric-teleparallel dark energy through the addition of a further Yukawa-like term, in which the non-metricity scalar, $Q$, is non-minimally coupled to a scalar field Lagrangian where the phion acts as quintessence,…
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…
This paper proposes a novel methodology for probabilistic dynamic security assessment and enhancement of power systems that considers load and generation variability, N-2 contingencies, and uncertain cascade propagation caused by uncertain…
We introduce a novel numerical approach for a class of stochastic dynamic programs which arise as discretizations of backward stochastic differential equations or semi-linear partial differential equations. Solving such dynamic programs…
Dynamical models for dark energy are an alternative to the cosmological constant. It is important to investigate properties of perturbations in these models and go beyond the smooth FRLW cosmology. This allows us to distinguish different…
In power system steady-state estimation (PSSE), one needs to consider (1) the need for robust statistics, (2) the nonconvex transmission constraints, (3) the fast-varying nature of the inputs, and the corresponding need to track optimal…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
We review some recent developments which make use of the concept of `superstatistics', an effective description for nonequilibrium systems with a varying intensive parameter such as the inverse temperature. We describe how the asymptotic…
Voltage stability in modern power systems involves coupled dynamics across multiple time scales. Conventional methods based on time-scale separation or static stability margins may overlook instabilities caused by the coupling of slow and…
Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…
Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels…
Employing model predictive control to systems with unbounded, stochastic disturbances poses the challenge of guaranteeing safety, i.e., repeated feasibility and stability of the closed-loop system. Especially, there are no strict repeated…
In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to…
Stochastic differential equations (SDE) often exhibit large random transitions. This property, which we denote as pathwise stiffness, causes transient bursts of stiffness which limit the allowed step size for common fixed time step explicit…
Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and…
This paper presents a discrete-time passivity-based analysis of the gradient descent method for a class of functions with sector-bounded gradients. Using a loop transformation, it is shown that the gradient descent method can be interpreted…
We present a detailed non-perturbative analysis of the time-evolution of a well-known quantum-mechanical system - a particle between potential walls - describing the decay of unstable states. For sufficiently high barriers, corresponding to…