A GLIMPSE OF NONLINEAR PHENOMENA FROM CHUAS OSCILLATOR

Chua's oscillator is a simple electronic circuit whose (dimensionless) state equations are given by dx/dt = k alpha(y - x - f(x)), dy/dt = k (x - y + z), dz/dt = k(-beta y - gamma z), where f(x) = bx + 1/2(a - b )[\x + 1\ - \x -1\]. It consists of two linear resistors, two linear c apacitors, one linear inductor and one nonlinear resistor. Chua's circ uit (which is Chua's oscillator with gamma = 0) can be built using dis crete components (figure 1a) or as an integrated circuit (figure 1b). The speed at which the circuit operates can be set by choosing appropr iate circuit component values. One of the advantages of Chua's oscilla tor is that the equations model the dynamical behaviour of the physica l system quite accurately. By varying the six parameters (alpha, beta, gamma, a, b, k) of Chua's oscillator various nonlinear phenomena such as bifurcations, self-similarity, and chaos can be observed. Many att ractors are found in Chua's oscillator by varying the parameters. Figu re 2 shows a geometric model of Chua's double-scroll chaotic attractor which is observed in Chua's oscillator. By coupling several Chua's os cillators in an array even more complicated phenomena can be observed. Figure 6a shows spiral waves and target waves interacting in an array of Chua's oscillators. Figure 6b shows a Turing pattern which is obse rved in an array of Chua's oscillators.