Lorenz system

The concept was the same as the Lorenz system.

As the German economy recovered, development of the Lorenz system was picked up again in the late 1930s.

This is the major stumbling block to experimental realisation of the Lorenz system in lasers.

From a technical standpoint, the Lorenz system is nonlinear, three-dimensional and deterministic.

The Lorenz system indicated the centreline of the two signals through the audio pattern, which was listened to by the navigator.

The Lorenz system worked by feeding a special three-element antenna system with a modulated radio signal.

The primary system developed for this role was the Lorenz system, which was in the process of being widely deployed on large civilian and military aircraft.

The Lorenz system is a reduced version of a larger system studied earlier by Barry Saltzman.

This method was applied to the Rössler system, and the Lorenz system, as well as thermal lens oscillations.

One is actually led to wonder what effect a knowledge of the Lorenz system, at an earlier stage, would have had on Smale's development of these important ideas.

As the antennas were physically separated, the spikes did not precisely overlap, producing the dots, dashes and equisignal zones of the Lorenz system.

When , , and , the Lorenz system has chaotic solutions (but not all solutions are chaotic).

In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure eight.

The Lorenz system (see eqn (2.2) and Chapter 6) has a complicated attractor, with trajectories spiralling around, and jumping between, two loops.

The Lorenz system was similar to the Diamond-Dunmore equi-signal radio guidance system, developed by the US Bureau of Standards in the early 1930s.

The Germans developed the short-range Lorenz system into the Knickebein aid, a system which used two Lorenz beams with much stronger signal transmissions.

The Lorenz system is a system of ordinary differential equations (the Lorenz equations) first studied by Edward Lorenz.

Strange attractors occur in both continuous dynamical systems (such as the Lorenz system) and in some discrete systems (such as the Hénon map).

But normal form arguments suggest that there is a dynamical system that is exponentially close to the Lorenz system for which there is a good slow manifold.

The bigeometric calculus was used in an article on multiplicative Lorenz systems by Dorota Aniszewska and Marek Rybaczuk (both from Wroclaw University of Technology).

A law of diminishing returns operates, such that to attain the sharpness achieved by the Lorenz system with a single beam (approximately 1 mile wide over a range of two hundred miles), an array of prohibitive size would be required.

Undamped relaxation oscillations had already been seen in such lasers, and at the time of writing there is the exciting prospect that the Lorenz system of equations may soon develop an experimental significance in laser physics to match their theoretical impact.

British intelligence at the Air Ministry, led by R V Jones, were aware of the system initially because a downed German bomber's Lorenz system was analysed by the Royal Aircraft Establishment and seen to be far too sensitive to be a mere landing aid.

Though excessive concentration on these equations can be criticised (since they are not, in many ways, typical of chaotic systems), it remains true that examples of nearly all the types of chaotic behaviour seen in other three-dimensional dissipative systems of differential equations can be found, for some parameter values, in the Lorenz system.