Bifurcation theory in discrete dynamical systems provides a rigorous framework for analysing qualitative changes in system behaviour as parameters vary. In these systems, subtle modifications of ...

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 ...

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 ...

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 ...

Dynamical systems provide a rigorous framework for understanding the evolution of complex systems over time, encapsulating models ranging from classical mechanical systems to chaotic and fractal ...

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 ...

This paper is a continuation of our study on doubly nonlinear parabolic type equations that was initiated by a previous paper; it is however self-contained. We propose here to investigate a time ...

Researchers from Osaka University have developed an artificial intelligence algorithm that discovers the underlying conservation laws of real-world dynamical systems, not just the superficial dynamics ...

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 ...