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We present an example of the practical implementation of a protocol for experimental bifurcation detection based on on-line identification and feedback control ideas. The idea is to couple the experiment with an on-line computer-assisted…

Forecasting system behaviour near and across bifurcations is crucial for identifying potential shifts in dynamical systems. While machine learning has recently been used to learn critical transitions and bifurcation structures from data,…

Diffusion models excel at modeling complex and multimodal trajectory distributions for decision-making and control. Reward-gradient guided denoising has been recently proposed to generate trajectories that maximize both a differentiable…

Boolean Delay Equations (BDEs) are semi-discrete dynamical models with Boolean-valued variables that evolve in continuous time. Systems of BDEs can be classified into conservative or dissipative, in a manner that parallels the…

This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such…

A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…

The numerical tools to simulate the bidomain model in cardiac electrophysiology are constantly developing due to the great clinical interest and scientific advances in mathematical models and computational power. The bidomain model consists…

Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the system's complexity increases and it is…

In this paper we propose a new methodology for decision-making under uncertainty using recent advancements in the areas of nonlinear stochastic optimal control theory, applied mathematics, and machine learning. Grounded on the fundamental…

Partial differential equations (PDEs) involving fractional Laplace operators have been increasingly used to model non-local diffusion processes and are actively investigated using both analytical and numerical approaches. The purpose of…

Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…

Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…

We report on Differential Evolution for Analytic Continuation (DEAC): a parameter-free evolutionary algorithm to generate the dynamic structure factor from imaginary time correlation functions. Our approach to this long-standing problem in…

The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic…

This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling…

Proposed here is a dynamic Monte-Carlo algorithm that is efficient in simulating dense systems of long flexible chain molecules. It expands on the configurational-bias Monte-Carlo method through the simultaneous generation of a large set of…

A challenging problem when studying a dynamical system is to find the interdependencies among its individual components. Several algorithms have been proposed to detect directed dynamical influences between time series. Two of the most used…

The energy consumption issue in distributed computing systems has become quite critical due to environmental concerns. In response to this, many energy-aware scheduling algorithms have been developed primarily by using the dynamic…

Sampling the phase space of molecular systems -- and, more generally, of complex systems effectively modeled by stochastic differential equations -- is a crucial modeling step in many fields, from protein folding to materials discovery.…

We propose an approach that links density functional theory (DFT) and molecular dynamics (MD) simulation to study fluid behavior in nanopores in contact with bulk (macropores). It consists of two principal steps. First, the theoretical…