Synchronization in a network of connected elements is essential to the proper functioning of
both natural and engineered systems and is thus of increasing interest across disciplines. In …

Chaotic time series data are observed routinely in experiments on physical systems and in
observations in the field. The authors review developments in the extraction of information of …

Continuous deep learning architectures have recently re-emerged as Neural Ordinary
Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the …

This work presents a two-dimensional (2-D) non-autonomous tabu learning single neuron
(TLSN) model based on sinusoidal activation function (SAF), which can generate a class of …

We present the first algorithms that allow the estimation of non-negative Lyapunov
exponents from an experimental time series. Lyapunov exponents, which provide a …

In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x;
µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and …

The paradigm of deterministic chaos has influenced thinking in many fields of science.
Chaotic systems show rich and surprising mathematical structures. In the applied sciences …

Metaphors, generalizations and unifications are natural and desirable ingredients of the
evolution of scientific theories and concepts. Physics, in particular, obviously walks along …

Over the past two decades scientists, mathematicians, and engineers have come to
understand that a large variety of systems exhibit complicated evolution with time. This …

A systematic examination of general three-dimensional autonomous ordinary differential
equations with quadratic nonlinearities has uncovered 19 distinct simple examples of …