A GLIMPSE OF NONLINEAR PHENOMENA FROM CHUAS OSCILLATOR

Chua's oscillator is a simple electronic circuit whose (dimensionless) state e 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 capacitors, one linear inductor and one nonlinear resistor. Chua's circuit (which is Chua's oscillator with gamma = 0) can be built using discrete components (figure 1a) or as an integrated circuit (figure 1b). The speed at which the circuit operates can be set by choosing appropriate circuit component values. One of the advantages of Chua's oscillator is that the equations model the dynamical behaviour of the physical 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 attractors are found in Chua's oscillator by varying the parameters. Figure 2 shows a geometric model of Chua's double-scroll chaotic attractor which is observed in Chua's oscillator. By coupling several Chua's oscillators 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 observed in an array of Chua's oscillators.