Download A gallery of Chua attractors by Eleanora Bilotta, Pietro Pantano PDF
By Eleanora Bilotta, Pietro Pantano
Chaos is taken into account as essentially the most vital ideas in sleek technology. It initially seemed basically in computing device simulation (the recognized Lorenz equation of 1963), yet this replaced with the advent of Chua s oscillator (1986) -- an easy digital circuit having the ability to generate an unlimited variety of chaotic behaviors. With Chua s circuit, chaos turned a actual phenomenon, quite simply understood and represented in mathematical language. but, nevertheless, it truly is nonetheless tricky for the non-specialist to understand the entire number of behaviors that the method can produce.
This ebook goals to bridge the distance. A gallery of approximately 900 chaotic attractors -- a few generated via Chua s actual circuit, the bulk via laptop simulation of the circuit and its generalizations -- are illustrated as 3D colour photos, time sequence and speedy Fourier remodel algorithms. For researchers, additionally offered is the knowledge essential to mirror the behaviors and pictures. ultimately, how the fractal richness may be plied to creative results in producing song and engaging sounds is proven; a few examples are incorporated within the DVD-ROM which comes with the publication.
Contents: Chua s Oscillator and Its Generations; The actual Circuit; Dimensionless Equations; The Cubic functionality; Single-Scroll structures; Multiscrolls platforms.
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Additional info for A gallery of Chua attractors
The PSD is shifted up in the frequency when compared to the previous signal. Fig. 5 ns and PRF=10 MHz The PSD of this signal has a smaller fractional bandwidth compared to the first derivative of the Gaussian pulse and it is higher in the frequency band. 3 Antennas for UWB Signals The antenna converts the electrical signals to electromagnetic waves that propagate in space. This conversion is frequency dependent and therefore the antenna acts as a filter. Depending on the frequency value, the antenna attenuates the signal amplitude and changes the signal delay.
At this frequency (or in a small bandwidth around this frequency) the gain is maximum and the antenna impedance is real. When the wavelength of the electromagnetic waves is different from this optimal wavelength the gain (in a given direction) is reduced and the antenna impedance is no longer real. Therefore, these types of antennas are bandpass systems and as such, will distort UWB signals. To understand this distortion, a dipole antenna (such as the ones depicted in Fig. 14) with a length equal to 25 cm, corresponding to a half-wavelength for a frequency approximately equal to 600 MHz, was used to perform the same analysis described before.
7 of the previous chapter. In order to fall under this narrow band condition when using short duration pulses, it is necessary to use a high carrier frequency. As an example, to identify targets separated by a distance smaller than 30 cm it is necessary to use a pulse with a duration inferior to 1 ns, this results that a carrier frequency larger than 20 GHz must be used in order to achieve a fractional bandwidth inferior to 10% , . Using a carrier signal with such a high frequency, requires that the circuits that process this signal must be constructed using expensive RF technologies, such as GaAs .