A simple nonlinear dynamical computing device

The Chaos Computing Paradigm

“…Also note that the system given by (1.1), realizable with the electronic circuit described in Figure 1.2, can also be utilized in a straightforward fashion to implement this storage and information processing method [13].…”

“…The voltage across resistor R1 is amplified by a factor of five using operational amplifier U1 in order to scale the output voltage back into the range of the input voltage, a necessary condition for a circuit based on a map. The resulting transfer characteristics of the nonlinear device are depicted in Figure 1.3 In Figure 1.2, the sample-and-hold circuits are realized with National Semiconductor's sample-and-hold IC LF398, triggered by delayed timing clock pulses CK1 and CK2 [13]. Here a clock rate of either 10 or 20 kHz may be used.…”

“…In subsequent years there has been much research activity to develop this paradigm [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. It was realized that one of the most promising directions of this computing paradigm was its ability to exploit a single chaotic element to reconfigure into different logic gates through a threshold-based morphing mechanism [3,4].…”

“…A simple nonlinear device is produced by coupling two complementary (n-channel and p-channel) junction field-effect transistors (JFETs) [13] mimicking the nonlinear characteristic curve f (x) = 2x/(1 + x 10 ). The circuit diagram is shown in Figure 1.2.…”

Unstable periodic orbits and noise in chaos computing

“…Furthermore, since a chaotic system exhibits different behaviors and patterns, it can implement different types of functions. [4][5][6][7][8][9][10][11][12][13] This flexibility of a chaotic system in building different types of functions comes at the expense of sensitivity to noise.…”