About the https://iris.unipa.it/retrieve/handle/10447/276402/535513/81-Minati_Chaos-2017.pdf I show a set of dynamic non linear equation that represent a good approximation of autonomous chaotic oscillator circuit. Chaos is a pervasive occurrence in these kind of circuits.
Analyzing the circuit using Kirchhoff's circuit laws, the dynamics of Transistor-based-chaotic-oscillator can be accurately modeled by means of a system of seven nonlinear ordinary differential equations:
C1 is B-C parasitic capacitance of NPN_1
C2 is B-E parasitic capacitance of NPN_1
C3 is C-E parasitic capacitance of NPN_2
And
The functions f(x) and g(x) describe the electrical response of the nonlinear component (transistor NPN), and its shape depends on the used model of its components.
Consider the base current too
The system become
A circuit model will always be an approximation of the real-world structure. An equivalent electrical circuit model is an idealized electrical description of a real structure. It is an approximation, based on using combinations of ideal circuit elements. In our case, after fists test, at the end we recognize:
Where:
C1 is the sum between parasitic capacitance of BJT Q1 and inductor L1
C2 is the parasitic capacitance of inductor L2
C3 is the sum between parasitic capacitance of BJT Q2 and parasitic capacitance of the left side circuit
Vdrop is the average voltage drop across the left side circuit
And, this time, the set of equations found are:
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