Chaotic maps are discrete-time systems with

chaotic behavior. It has been theoretically proven that the numbers produced by chaotic maps have unpredictable, spread spectral characteristics and are not periodic [21].

Within the circuit experiencing

chaotic behavior are several branches of current and several nodes of voltage with respect to the circuit ground.

By varying parameter b from 2.87 to 3.8, the bifurcation diagram of the output x(t) in Figure 5(a) displays

chaotic behavior interspersed with periodic windows.

The particular features of these two descriptors characterize the

chaotic behavior. The Poincaree map contains an infinite set of points, which are referred to as a strange attractor.

For [alpha] = 1, to analyze the

chaotic behavior of traffic-flow evolution with [theta] and [phi], the different states of the evolution with [theta] and [phi] are plotted using numerical experiments for [lambda] = 0.4, as shown in the left figure of Figure 5(a).

One particular case are the systems with negative feedback which exhibit

chaotic behavior under specific structural conditions.

Figure 16 shows first two return maps, where the

chaotic behavior can be seen on one hand and, on the other hand, the regular behavior can be seen.

Since long ago it is known that certain chemical reactions oscillate and now traces of

chaotic behavior in some of those reactions have been identified.

They concluded that the

chaotic behavior of the system can be used to simulate the reversals of the geomagnetic field.

Drawing on existing tests of nonlinearities and chaos, we first investigate the existence of

chaotic behavior as the source of nonlinearities in the monthly prices of jet fuel and a measure of yield in the air carrier industry, dollars per revenue passenger miles.

with [beta] between 3.57 and 4.0 [13], Its

chaotic behavior has been widely studied and several generators have already used such logistic map for generating pseudo-random numbers f 14, 15, 16, 17], To avoid non-chaotic behaviour (island of stability, oscillations, ...), the value of [beta] should be near 4.0, which corresponds to a highly chaotic behaviour.

Circuits of nonlinear dynamic system provide an excellent tool for the study of

chaotic behavior. Some of these circuits treat time as a discrete variable, employing sample-and-hold subcircuits and analog multipliers to model iterated maps such as the logistic map [5, 6].