ChuaCircuit ​
Chua's circuit, an electronic circuit known for its chaotic dynamics.
This component represents Chua's circuit, a relatively simple electronic system capable of exhibiting complex nonlinear dynamics, including bifurcations and chaos. The circuit is constructed from two capacitors (capacitor1, capacitor2), one inductor (inductor), a linear resistor (resistor), a linear conductor (conductor), and a single nonlinear element known as Chua's diode (represented by nonlinear_resistor). The behavior of the circuit is typically described by a set of three first-order autonomous ordinary differential equations for the voltage across each capacitor and the current through the inductor.
The current i_NR through the nonlinear_resistor as a function of the voltage v_C1 across it is given by:
The governing differential equations for the circuit are (using v_C1 for capacitor1.v, v_C2 for capacitor2.v, i_L for inductor.i):
Initial conditions for capacitor1.v, capacitor2.v, and inductor.i are specified within the relations block to define the starting state of the simulation.
Usage ​
ElectricalComponents.ChuaCircuit()
Behavior ​
julia
using ElectricalComponents #hide
using ModelingToolkit #hide
@named sys = ElectricalComponents.ChuaCircuit() #hide
full_equations(sys) #hide<< @example-block not executed in draft mode >>Source ​
dyad
"""
Chua's circuit, an electronic circuit known for its chaotic dynamics.
This component represents Chua's circuit, a relatively simple electronic system
capable of exhibiting complex nonlinear dynamics, including bifurcations and
chaos. The circuit is constructed from two capacitors (`capacitor1`, `capacitor2`),
one inductor (`inductor`), a linear resistor (`resistor`), a linear conductor
(`conductor`), and a single nonlinear element known as Chua's diode (represented
by `nonlinear_resistor`). The behavior of the circuit is typically described by a
set of three first-order autonomous ordinary differential equations for the
voltage across each capacitor and the current through the inductor.
The current `i_NR` through the `nonlinear_resistor` as a function of the voltage `v_C1` across it is given by:math i_{NR}(v_{C1}) = Gb \cdot v_{C1} + \frac{1}{2}(Ga - Gb)(|v_{C1} + Ve| - |v_{C1} - Ve|)
The governing differential equations for the circuit are (using `v_C1` for `capacitor1.v`, `v_C2` for `capacitor2.v`, `i_L` for `inductor.i`):math capacitor1.C \cdot \frac{d(v_{C1})}{dt} = conductor.G \cdot (v_{C2} - v_{C1}) - i_{NR}(v_{C1})
math capacitor2.C \cdot \frac{d(v_{C2})}{dt} = conductor.G \cdot (v_{C1} - v_{C2}) - i_L
math inductor.L \cdot \frac{d(i_L)}{dt} = v_{C2} - resistor.R \cdot i_L
Initial conditions for `capacitor1.v`, `capacitor2.v`, and `inductor.i` are
specified within the `relations` block to define the starting state of the simulation.
"""
component ChuaCircuit
"Inductor of the Chua's circuit."
inductor = Inductor(L = 18) {
"Dyad": {"placement": {"icon": {"x1": 0, "y1": 200, "x2": 200, "y2": 400, "rot": 90}}}
}
"Linear resistor, typically in series with the inductor."
resistor = Resistor(R = 12.5e-3) {
"Dyad": {"placement": {"icon": {"x1": 0, "y1": 500, "x2": 200, "y2": 700, "rot": 90}}}
}
"Linear conductor, connecting the two capacitors."
conductor = Conductor(G = 0.565) {
"Dyad": {"placement": {"icon": {"x1": 450, "y1": 50, "x2": 650, "y2": 250, "rot": 0}}}
}
"First capacitor in the Chua's circuit."
capacitor1 = Capacitor(C = 10) {
"Dyad": {"placement": {"icon": {"x1": 600, "y1": 350, "x2": 800, "y2": 550, "rot": 90}}}
}
"Second capacitor in the Chua's circuit."
capacitor2 = Capacitor(C = 100) {
"Dyad": {"placement": {"icon": {"x1": 300, "y1": 350, "x2": 500, "y2": 550, "rot": 90}}}
}
"Nonlinear resistor representing the Chua's diode, with parameters Ga, Gb, Ve."
nonlinear_resistor = NonlinearResistor(Ga = -0.757576, Gb = -0.409091, Ve = 1) {
"Dyad": {
"placement": {"icon": {"x1": 900, "y1": 350, "x2": 1100, "y2": 550, "rot": 90}}
}
}
"Ground reference for the circuit."
ground = Ground() {
"Dyad": {"placement": {"icon": {"x1": 450, "y1": 800, "x2": 650, "y2": 1000, "rot": 0}}}
}
relations
initial inductor.i = 0
initial capacitor1.v = 4
initial capacitor2.v = 0
connect(inductor.n, resistor.p) {"Dyad": {"edges": [{"S": 1, "E": 2}]}}
connect(inductor.p, capacitor2.p, conductor.p) {
"Dyad": {
"edges": [
{"S": -1, "M": [{"x": 100, "y": 150}], "E": 1},
{"S": -1, "E": 2},
{"S": -1, "E": 3}
],
"junctions": [{"x": 400, "y": 150}]
}
}
connect(conductor.n, nonlinear_resistor.p, capacitor1.p) {
"Dyad": {
"edges": [
{"S": -1, "E": 1},
{"S": -1, "M": [{"x": 1000, "y": 150}], "E": 2},
{"S": -1, "E": 3}
],
"junctions": [{"x": 700, "y": 150}]
}
}
connect(ground.g, resistor.n, capacitor2.n, capacitor1.n, nonlinear_resistor.n) {
"Dyad": {
"edges": [
{"S": -1, "E": 1},
{"S": -1, "M": [{"x": 100, "y": 750}], "E": 2},
{"S": -1, "M": [{"x": 400, "y": 750}], "E": 3},
{"S": -1, "M": [{"x": 700, "y": 750}], "E": 4},
{"S": -1, "M": [{"x": 1000, "y": 750}], "E": 5}
],
"junctions": [{"x": 550, "y": 750}]
}
}
metadata {
"Dyad": {"tests": {"case1": {"stop": 50000, "expect": {"signals": ["capacitor1.v"]}}}}
}
endFlattened Source
dyad
"""
Chua's circuit, an electronic circuit known for its chaotic dynamics.
This component represents Chua's circuit, a relatively simple electronic system
capable of exhibiting complex nonlinear dynamics, including bifurcations and
chaos. The circuit is constructed from two capacitors (`capacitor1`, `capacitor2`),
one inductor (`inductor`), a linear resistor (`resistor`), a linear conductor
(`conductor`), and a single nonlinear element known as Chua's diode (represented
by `nonlinear_resistor`). The behavior of the circuit is typically described by a
set of three first-order autonomous ordinary differential equations for the
voltage across each capacitor and the current through the inductor.
The current `i_NR` through the `nonlinear_resistor` as a function of the voltage `v_C1` across it is given by:math i_{NR}(v_{C1}) = Gb \cdot v_{C1} + \frac{1}{2}(Ga - Gb)(|v_{C1} + Ve| - |v_{C1} - Ve|)
The governing differential equations for the circuit are (using `v_C1` for `capacitor1.v`, `v_C2` for `capacitor2.v`, `i_L` for `inductor.i`):math capacitor1.C \cdot \frac{d(v_{C1})}{dt} = conductor.G \cdot (v_{C2} - v_{C1}) - i_{NR}(v_{C1})
math capacitor2.C \cdot \frac{d(v_{C2})}{dt} = conductor.G \cdot (v_{C1} - v_{C2}) - i_L
math inductor.L \cdot \frac{d(i_L)}{dt} = v_{C2} - resistor.R \cdot i_L
Initial conditions for `capacitor1.v`, `capacitor2.v`, and `inductor.i` are
specified within the `relations` block to define the starting state of the simulation.
"""
component ChuaCircuit
"Inductor of the Chua's circuit."
inductor = Inductor(L = 18) {
"Dyad": {"placement": {"icon": {"x1": 0, "y1": 200, "x2": 200, "y2": 400, "rot": 90}}}
}
"Linear resistor, typically in series with the inductor."
resistor = Resistor(R = 12.5e-3) {
"Dyad": {"placement": {"icon": {"x1": 0, "y1": 500, "x2": 200, "y2": 700, "rot": 90}}}
}
"Linear conductor, connecting the two capacitors."
conductor = Conductor(G = 0.565) {
"Dyad": {"placement": {"icon": {"x1": 450, "y1": 50, "x2": 650, "y2": 250, "rot": 0}}}
}
"First capacitor in the Chua's circuit."
capacitor1 = Capacitor(C = 10) {
"Dyad": {"placement": {"icon": {"x1": 600, "y1": 350, "x2": 800, "y2": 550, "rot": 90}}}
}
"Second capacitor in the Chua's circuit."
capacitor2 = Capacitor(C = 100) {
"Dyad": {"placement": {"icon": {"x1": 300, "y1": 350, "x2": 500, "y2": 550, "rot": 90}}}
}
"Nonlinear resistor representing the Chua's diode, with parameters Ga, Gb, Ve."
nonlinear_resistor = NonlinearResistor(Ga = -0.757576, Gb = -0.409091, Ve = 1) {
"Dyad": {
"placement": {"icon": {"x1": 900, "y1": 350, "x2": 1100, "y2": 550, "rot": 90}}
}
}
"Ground reference for the circuit."
ground = Ground() {
"Dyad": {"placement": {"icon": {"x1": 450, "y1": 800, "x2": 650, "y2": 1000, "rot": 0}}}
}
relations
initial inductor.i = 0
initial capacitor1.v = 4
initial capacitor2.v = 0
connect(inductor.n, resistor.p) {"Dyad": {"edges": [{"S": 1, "E": 2}]}}
connect(inductor.p, capacitor2.p, conductor.p) {
"Dyad": {
"edges": [
{"S": -1, "M": [{"x": 100, "y": 150}], "E": 1},
{"S": -1, "E": 2},
{"S": -1, "E": 3}
],
"junctions": [{"x": 400, "y": 150}]
}
}
connect(conductor.n, nonlinear_resistor.p, capacitor1.p) {
"Dyad": {
"edges": [
{"S": -1, "E": 1},
{"S": -1, "M": [{"x": 1000, "y": 150}], "E": 2},
{"S": -1, "E": 3}
],
"junctions": [{"x": 700, "y": 150}]
}
}
connect(ground.g, resistor.n, capacitor2.n, capacitor1.n, nonlinear_resistor.n) {
"Dyad": {
"edges": [
{"S": -1, "E": 1},
{"S": -1, "M": [{"x": 100, "y": 750}], "E": 2},
{"S": -1, "M": [{"x": 400, "y": 750}], "E": 3},
{"S": -1, "M": [{"x": 700, "y": 750}], "E": 4},
{"S": -1, "M": [{"x": 1000, "y": 750}], "E": 5}
],
"junctions": [{"x": 550, "y": 750}]
}
}
metadata {
"Dyad": {"tests": {"case1": {"stop": 50000, "expect": {"signals": ["capacitor1.v"]}}}}
}
endTest Cases ​
julia
using ElectricalComponents
using DyadInterface: TransientAnalysis, rebuild_sol
using ModelingToolkit: toggle_namespacing, get_defaults, @named
using CSV, DataFrames, Plots
snapshotsdir = joinpath(dirname(dirname(pathof(ElectricalComponents))), "test", "snapshots")<< @setup-block not executed in draft mode >>Test Case case1 ​
julia
@named model_case1 = ChuaCircuit()
model_case1 = toggle_namespacing(model_case1, false)
model_case1 = toggle_namespacing(model_case1, true)
result_case1 = TransientAnalysis(; model = model_case1, alg = "auto", start = 0e+0, stop = 5e+4, abstol=1e-6, reltol=1e-6)
sol_case1 = rebuild_sol(result_case1)<< @setup-block not executed in draft mode >>julia
df_case1 = DataFrame(:t => sol_case1[:t], :actual => sol_case1[model_case1.capacitor1.v])
dfr_case1 = try CSV.read(joinpath(snapshotsdir, "ChuaCircuit_case1_sig0.ref"), DataFrame); catch e; nothing; end
plt = plot(sol_case1, idxs=[model_case1.capacitor1.v], width=2, label="Actual value of capacitor1.v")
if !isnothing(dfr_case1)
scatter!(plt, dfr_case1.t, dfr_case1.expected, mc=:red, ms=3, label="Expected value of capacitor1.v")
end<< @setup-block not executed in draft mode >>julia
plt<< @example-block not executed in draft mode >>Related ​
Examples
Experiments
Analyses