At each sampling time instant, one observes system output and action to form discrete-time rewards. The sampled input-output data are collected along the trajectory of the dynamical system in ...

Ordinary differential equations (ODEs), difference equations and dynamical systems provide complementary frameworks for modelling the evolution of quantities in continuous or discrete time. ODEs ...

Computers have helped us prove many theorems, which like the four-color theorem are mostly combinatorial or discrete in nature. For domains like dynamical systems, however, computer-assisted proofs ...

Antifragility characterizes the benefit of a dynamical system derived from the variability in environmental perturbations. Antifragility carries a precise definition that quantifies a system’s output ...

The application of dynamical systems theory to areas outside of mathematics continues to be a vibrant, exciting, and fruitful endeavor. These application areas are diverse and multidisciplinary, ...

We often encounter nonlinear dynamical systems that behave unpredictably, such as the Earth's climate and the stock market. To analyze them, measurements taken over time are used to reconstruct the ...