This paper reviews the major developments of modeling techniques applied to nonlinear
dynamics and chaos. Model representations, parameter estimation techniques, data …

This article compares the pros and cons of using prediction error and simulation error to
define cost functions for parameter estimation in the context of nonlinear system …

Forecasting the solar cycle is of great importance for weather prediction and environmental
monitoring, and also constitutes a difficult scientific benchmark in nonlinear dynamical …

Identifying chaos in experimental data—noisy data—remains a challenging problem for
which conclusive arguments are still very difficult to provide. In order to avoid problems …

This paper reviews some aspects of nonlinear model building from data with (gray box) and
without (black box) prior knowledge. The model class is very important because it …

When a global model is attempted from experimental data, some preprocessing might be
required. Therefore it is only natural to wonder what kind of effects the preprocessing might …

Synchronizing nonidentical chaotic oscillators is very often achieved by using various types
of couplings. In the practice of synchronization the “right choice” of the coupling variable—y …

This paper is concerned with the numerical solution of fractional initial value problems
(FIVP) in sense of Caputo's definition for dynamical systems. Unlike for integer-order …

We introduce a new method for predicting characteristics of the synchronized state achieved
by a wide class of unidirectional coupling schemes. Specifically, we derive a transfer …

We propose a method for extracting general features from multivariate data using a network
of phase oscillators subject to an analogue of the Kuramoto model for collective …