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) and difference equations serve as complementary tools in the mathematical modelling of processes evolving in continuous and discrete time respectively. Together ...

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 ...

Random walks serve as an important tool in the complex networks community due to widespread applications including Google’ PageRank algorithm, community detection, network exploration, and modeling ...

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 ...

Scientists usually use a hypergraph model to predict dynamic behaviors. But the opposite problem is interesting, too. What if researchers can observe the dynamics but don't have access to a reliable ...

Transactions of the American Mathematical Society, Vol. 365, No. 10 (OCTOBER 2013), pp. 5329-5365 (37 pages) This series of papers is concerned with principal Lyapunov exponents and principal Floquet ...

There has recently been considerable interest in both applied disciplines and in mathematics, as well as in the popular science literature, in the areas of nonlinear dynamical systems and chaotic ...