The advent of the feed-forward neural network (N) model opens the possibility of hybrid neural–dynamical models via variational data assimilation. Such a hybrid model may be used in situations where some variables, difficult to model dynamically, have sufficient data for modeling them empirically with an N. This idea of using an N to replace missing dynamical equations is tested with the Lorenz...

This paper describes the LMI synthesis of feedback controllers which minimise closed loop transient perturbation growth with limited control effort. Controllers are synthesized for the linearised Lorenz equations, and their performance is compared to that of LQR controllers. At low control effort the controllers behave similarly, but the LMI based controllers are able to produce an almost monot...

In general, chaotic dynamical systems produce ill-conditioned direct and adjoint sensitivity equations, so these conventional sensitivity analysis methods do not provide useful derivatives for design optimization of chaotic systems. The least-squares shadowing (LSS) method is a recently proposed regularization of the sensitivity equations that leads to useful derivative information; however, th...

In the present paper we report experimental observations of discrete spatiotemporal structures in rings of unidirectionally coupled analog Lorenz systems. This is an extension of the results previously reported in [Sánchez & Mat́ıas, 1998], studying now other parameter regimes. These studies are based on the use of an analog circuit corresponding to Lorenz equations. The more interesting new res...

Lorenz’s mathematical model of the weather, made in 1963, describes the motion of the air through the atmosphere. More precisely, Lorenz observed the hot air rising up into the atmosphere, then cooling down and eventually falling to the ground. While observing the weather conditions, Lorenz noticed that the weather does not always behave in a foreseen manner. In his attempt of introducing a mat...

Before the advent of modern computers, mathematicians used analog circuits to model non-integrable differential equations. This paper investigates the feasibility, functionality, and accuracy of several systems including the solar system, three-body system, and Lorenz attractor. Due to their highly nonlinear nature and circuit limitations, the solar system and three-body systems are not practic...

Using the Lorenz equations, we have investigated whether unstable periodic orbits (UPOs) associated with a strange attractor may predict the occurrence of the robust sharp peaks in histograms of some experimental chaotic time series. Histograms with sharp peaks occur for the Lorenz parameter value r = 60.0 but not for r = 28.0, and the sharp peaks for r = 60.0 do not correspond to any single hi...