Chua's circuit

Chua 's circuit is a simple electronic circuit for the first time in 1983 by Leon. O Chua was described and published in 1984. The circuit has chaotic behavior and is suitable as a demonstration for effects of chaos theory and nonlinear dynamics.

Electronic structure

The adjacent circuit diagram shows Chua 's Circuit. The operational amplifier OPA, together with the two 290 ohm resistors, a negative resistance (NIC). Together with the left circuit part to an oscillating circuit forms. Now, however, is when the amplitude of oscillation exceeds the breakdown voltage of the diodes D1, D2 connected (both in the positive and in the negative half cycle ), one of the resistors R2 connected in parallel to the negative resistance.

The system described differential equation is thus not linear and the dynamics of the system, the typical effects of chaotic systems, such as bifurcation and a strange attractor. The behavior of the present system is generally described as a function of resistance R as a chaos parameters.

Theoretical description

Chua 's circuit can be mathematically very simply described with the help of Kirchhoff's rules. For this purpose one chooses, for example, the voltages on the two capacitors UC1 and UC2, and the coil current IL as dynamic variables that span the phase space. The behavior of the non-linear resistor can be modeled with a function g ( UC1 ), which shows the current-voltage characteristic. It should be noted here that the non- linear resistor is applied the same voltage as the capacitor C1.

By applying the rule node to the nodes on the two capacitors is obtained

From the mesh usually obtained

This system of differential equations characterizing the entire dynamics of the system. The solution which is a trajectory in the phase space, for given initial conditions, the time evolution of the system described, in which each time the state of the system is given by a point in phase space. Since the Lösungstrakjektorie is clearly the behavior of Chua 's Circuit is strictly deterministic.

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