Download/Embed scientific diagram | 2: Plot degli attrattori di Lorenz from publication: Un TRNG basato sulla Teoria del Caos | Keywords. This Pin was discovered by Patricia Schappler. Discover (and save!) your own Pins on Pinterest. All’inizio di questo testo ho già premesso che la forma predominante nel nostro deducibile dalle varie rappresentazioni della legge dell’attrattore di Lorenz e.
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In the time domain, it becomes apparent that although each variable is oscillating within a fixed range of values, the oscillations are chaotic. This attractor has some ahtrattore to the Lorenz attractor, but is simpler and has only one manifold.
Another line of the parameter space was investigated using the topological analysis.
This yields the general equations of each of the fixed point coordinates:. The stability of each of these fixed points can be analyzed by determining their respective eigenvalues and eigenvectors.
Beginning with the Jacobian:.
The magnitude of a negative eigenvalue characterizes the level of attraction along the corresponding eigenvector. Similarly the magnitude of a positive eigenvalue attarttore the level of repulsion along the corresponding eigenvector.
Lorenz system – Wikipedia
These eigenvectors have several interesting implications. This effect is roughly demonstrated with the figure below. The figure examines the central fixed point eigenvectors.
As the resulting sequence approaches the central fixed point and the attractor itself, the influence of this distant fixed point and its eigenvectors will wane.
When visualized, the plot resembled the tent mapimplying that similar analysis can be used between the map and attractor. The bifurcation diagram is specifically a useful analysis method. In general, varying each parameter has a comparable effect by causing the system to converge toward a periodic orbit, fixed point, or escape towards infinity, however the specific ranges and behaviors induced vary substantially for each parameter.
They are created by running the equations of the system, holding all but one of the variables constant and varying the last one. Then, a graph is plotted of the points that a particular value for the changed variable visits after transient factors have been neutralised.
Chaotic regions are indicated by filled-in regions of the plot.
The results of the analysis are:. From Wikipedia, the free encyclopedia. This article needs additional citations for verification.
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