.ChaoticCircuits.ChaoticDiode .ChaoticCircuits.ChaoticDiodeThis is a simple chaotic example with a light-emitting diode (and 4 operational amplifiers) as described in [Pham2016] .
A novel simple autonomous optoelectronic chaotic circuit is presented in this work. Interestingly, the circuit is based on a single optoelectronic element, a light-emitting diode. The mathematical model of the circuit is described by three first-order ordinary differential equations which contain six terms with two parameters and an exponential nonlinearity. The proposed circuit is easy to be implemented by using common cheap components. The circuit can exhibit complex dynamical behavior like chaos despite of its simplicity. Therefore, it is a potential candidate for chaos-based engineering applications or is intended for educational purposes.
In this model, the proposed circuit is modeled using components from the Modelica Standard Library:
The parameters as calculated as described in the paper: Choosing the time constant Tau and the capacitance C as well as the dimensionless parameters a and b, all resistances are caculated using the parameters of the diode nVt and Ids.
Plot x[2] vs. x[1], x[3] vs. x[1] and x[3] vs. x[2].
Default parameter b = 1.5 (i.e. Rb = 6666.67 Ω) shows periodic results.
Change parameter b = 1.0 (i.e. Rb = 10 kΩ) to obtain chaotic results.
Note that an initial condition is necessary.
Note: In detail, the results of this model may differ from the results shown in the mentioned paper, especially in the region of chaotic results, because the diode model is similar but more detailed than the pure Shockley equation used in the paper
i = Ids*(exp(v/nVt) - 1)| Name | Description |
|---|---|
 AnalyticEquations | Analytic equations of the chaotic diode circuit |
 IdealCircuit | A simple chaotic circuit with a light-emitting diode |
 ImprovedCircuit | A simple chaotic circuit with a light-emitting diode |