1. Demonstration of Chaos Circuits Sajjad

2. Circuit Diagram + - + - 30.8  58 mH 330  2K  3.3K  20K  5K  0.4  F 0.033  F 1 2 3 TL087 Negative resistance - 1 Negative resistance - 2 LC tank circuit Critical control For CHAOS

3. Negative Resistance + - 330  2K  3 2 6 7 TL087 mA V V I 4 Negative resistance I

4. Nonlinear negative resistance + - 330  2K  3 2 6 7 TL087 mA V 4 + - 20K  3.3K  3 2 6 7 TL087 4 Parallel Negative resistance

5. Damped and undamped oscillation + - 330  2K  3 2 6 7 TL087 4 5K  0.1  F Find: L = ? R L = ? RLRL L One negative resistance is connected to a LC tank circuit with some losses in the internal resistance Of the inductor L. Connecting the negative resistance, forces the oscillation to continue Oscillation will stop if this value is bigger than the negative resistance

6. V-I Characteristics of parallel NR Negative resistance - 1 Negative resistance - 2 Parallel Negative resistance Break points Critical adjustment of Resistance “R” stops Oscillation at these “Break points”. Then Oscillation can start from any point close to Origin and go either negative or positive Direction, which is chaotic.

7. The state equations G = 1/R g is a piecewise linear function defined by: R C2C2 C1C1 NRNR

8. Final circuit diagram with values + - + - 30.8  58 mH 330  2K  3.3K  20K  5K  0.4  F 0.033  F CH1 CH2 oscilloscope TL087

9. Oscilloscope traces Y-t X-Y

10. Photograph of the fabricated circuit