LIBRARY

Analog.Examples.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:

$$i_{NR}(v_{C1})=Gb\cdot v_{C1}+\frac{1}{2}(Ga-Gb)(|v_{C1}+Ve|-|v_{C1}-Ve|)$$

The governing differential equations for the circuit are (using v_C1 for capacitor1.v, v_C2 for capacitor2.v, i_L for inductor.i):

$$capacitor1.C\cdot \frac{d(v_{C1})}{dt}=conductor.G\cdot (v_{C2}-v_{C1})-i_{NR}(v_{C1})$$$$capacitor2.C\cdot \frac{d(v_{C2})}{dt}=conductor.G\cdot (v_{C1}-v_{C2})-i_L$$$$inductor.L\cdot \frac{d(i_L)}{dt}=v_{C2}-resistor.R\cdot i_L$$

Initial conditions for capacitor1.v, capacitor2.v, and inductor.i are specified within the relations block to define the starting state of the simulation.

Usage

ElectricalComponents.Analog.Examples.ChuaCircuit()

Behavior

using ElectricalComponents #hide
using ModelingToolkit #hide
@named sys = ElectricalComponents.Analog.Examples.ChuaCircuit() #hide
full_equations(sys) #hide

<< @example-block not executed in draft mode >>

Source

"""
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.
"""
example component ChuaCircuit
  "Inductor of the Chua's circuit."
  inductor = ElectricalComponents.Analog.Basic.Inductor(L = 18) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 0, "y1": 100, "x2": 100, "y2": 200, "rot": 90},
        "diagram": {"iconName": "default", "x1": 60, "y1": 120, "x2": 160, "y2": 220, "rot": 90}
      },
      "tags": []
    }
  }
  "Linear resistor, typically in series with the inductor."
  resistor = ElectricalComponents.Analog.Basic.Resistor(R = 12.5e-3) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 0, "y1": 250, "x2": 100, "y2": 350, "rot": 90},
        "diagram": {"iconName": "default", "x1": 60, "y1": 300, "x2": 160, "y2": 400, "rot": 90}
      },
      "tags": []
    }
  }
  "Linear conductor, connecting the two capacitors."
  conductor = ElectricalComponents.Analog.Basic.Conductor(G = 0.565) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 225, "y1": 25, "x2": 325, "y2": 125, "rot": 0},
        "diagram": {"iconName": "default", "x1": 460, "y1": 20, "x2": 560, "y2": 120, "rot": 0}
      },
      "tags": []
    }
  }
  "First capacitor in the Chua's circuit."
  capacitor1 = ElectricalComponents.Analog.Basic.Capacitor(C = 10) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 300, "y1": 175, "x2": 400, "y2": 275, "rot": 90},
        "diagram": {"iconName": "default", "x1": 700, "y1": 180, "x2": 800, "y2": 280, "rot": 90}
      },
      "tags": []
    }
  }
  "Second capacitor in the Chua's circuit."
  capacitor2 = ElectricalComponents.Analog.Basic.Capacitor(C = 100) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 150, "y1": 175, "x2": 250, "y2": 275, "rot": 90},
        "diagram": {"iconName": "default", "x1": 270, "y1": 190, "x2": 370, "y2": 290, "rot": 90}
      },
      "tags": []
    }
  }
  "Nonlinear resistor representing the Chua's diode, with parameters Ga, Gb, Ve."
  nonlinear_resistor = ElectricalComponents.Analog.Basic.NonlinearResistor(Ga = -0.757576, Gb = -0.409091, Ve = 1) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 450, "y1": 175, "x2": 550, "y2": 275, "rot": 90},
        "diagram": {"iconName": "default", "x1": 880, "y1": 180, "x2": 980, "y2": 280, "rot": 90}
      },
      "tags": []
    }
  }
  "Ground reference for the circuit."
  ground = ElectricalComponents.Analog.Basic.Ground() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 225, "y1": 400, "x2": 325, "y2": 500, "rot": 0},
        "diagram": {"iconName": "default", "x1": 450, "y1": 500, "x2": 550, "y2": 600, "rot": 0}
      },
      "tags": []
    }
  }
relations
  initial inductor.i = 0
  initial capacitor1.v = 4
  initial capacitor2.v = 0
  connect(inductor.n, resistor.p) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(conductor.p, inductor.p) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 110, "y": 70}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(nonlinear_resistor.p, conductor.n) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 930, "y": 70}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(capacitor2.n, resistor.n) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 320, "y": 460}, {"x": 110, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(capacitor1.p, conductor.n) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 750, "y": 70}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(inductor.p, capacitor2.p) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 110, "y": 70}, {"x": 320, "y": 70}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(ground.g, resistor.n) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 500, "y": 460}, {"x": 110, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(capacitor1.n, ground.g) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 750, "y": 460}, {"x": 500, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(nonlinear_resistor.n, ground.g) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 930, "y": 460}, {"x": 500, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "icons": {"default": "dyad://ElectricalComponents/Example.svg"},
    "tests": {
      "case1": {
        "stop": 200,
        "reltol": 1e-9,
        "abstol": 1e-9,
        "expect": {"signals": ["capacitor1.v"]}
      }
    }
  }
}
end

Flattened Source

"""
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.
"""
example component ChuaCircuit
  "Inductor of the Chua's circuit."
  inductor = ElectricalComponents.Analog.Basic.Inductor(L = 18) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 0, "y1": 100, "x2": 100, "y2": 200, "rot": 90},
        "diagram": {"iconName": "default", "x1": 60, "y1": 120, "x2": 160, "y2": 220, "rot": 90}
      },
      "tags": []
    }
  }
  "Linear resistor, typically in series with the inductor."
  resistor = ElectricalComponents.Analog.Basic.Resistor(R = 12.5e-3) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 0, "y1": 250, "x2": 100, "y2": 350, "rot": 90},
        "diagram": {"iconName": "default", "x1": 60, "y1": 300, "x2": 160, "y2": 400, "rot": 90}
      },
      "tags": []
    }
  }
  "Linear conductor, connecting the two capacitors."
  conductor = ElectricalComponents.Analog.Basic.Conductor(G = 0.565) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 225, "y1": 25, "x2": 325, "y2": 125, "rot": 0},
        "diagram": {"iconName": "default", "x1": 460, "y1": 20, "x2": 560, "y2": 120, "rot": 0}
      },
      "tags": []
    }
  }
  "First capacitor in the Chua's circuit."
  capacitor1 = ElectricalComponents.Analog.Basic.Capacitor(C = 10) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 300, "y1": 175, "x2": 400, "y2": 275, "rot": 90},
        "diagram": {"iconName": "default", "x1": 700, "y1": 180, "x2": 800, "y2": 280, "rot": 90}
      },
      "tags": []
    }
  }
  "Second capacitor in the Chua's circuit."
  capacitor2 = ElectricalComponents.Analog.Basic.Capacitor(C = 100) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 150, "y1": 175, "x2": 250, "y2": 275, "rot": 90},
        "diagram": {"iconName": "default", "x1": 270, "y1": 190, "x2": 370, "y2": 290, "rot": 90}
      },
      "tags": []
    }
  }
  "Nonlinear resistor representing the Chua's diode, with parameters Ga, Gb, Ve."
  nonlinear_resistor = ElectricalComponents.Analog.Basic.NonlinearResistor(Ga = -0.757576, Gb = -0.409091, Ve = 1) {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 450, "y1": 175, "x2": 550, "y2": 275, "rot": 90},
        "diagram": {"iconName": "default", "x1": 880, "y1": 180, "x2": 980, "y2": 280, "rot": 90}
      },
      "tags": []
    }
  }
  "Ground reference for the circuit."
  ground = ElectricalComponents.Analog.Basic.Ground() {
    "Dyad": {
      "placement": {
        "icon": {"iconName": "default", "x1": 225, "y1": 400, "x2": 325, "y2": 500, "rot": 0},
        "diagram": {"iconName": "default", "x1": 450, "y1": 500, "x2": 550, "y2": 600, "rot": 0}
      },
      "tags": []
    }
  }
relations
  initial inductor.i = 0
  initial capacitor1.v = 4
  initial capacitor2.v = 0
  connect(inductor.n, resistor.p) {"Dyad": {"edges": [{"S": 1, "M": [], "E": 2}], "renderStyle": "standard"}}
  connect(conductor.p, inductor.p) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 110, "y": 70}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(nonlinear_resistor.p, conductor.n) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 930, "y": 70}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(capacitor2.n, resistor.n) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 320, "y": 460}, {"x": 110, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(capacitor1.p, conductor.n) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 750, "y": 70}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(inductor.p, capacitor2.p) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 110, "y": 70}, {"x": 320, "y": 70}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(ground.g, resistor.n) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 500, "y": 460}, {"x": 110, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(capacitor1.n, ground.g) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 750, "y": 460}, {"x": 500, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
  connect(nonlinear_resistor.n, ground.g) {
    "Dyad": {
      "edges": [{"S": 1, "M": [{"x": 930, "y": 460}, {"x": 500, "y": 460}], "E": 2}],
      "renderStyle": "standard"
    }
  }
metadata {
  "Dyad": {
    "icons": {"default": "dyad://ElectricalComponents/Example.svg"},
    "tests": {
      "case1": {
        "stop": 200,
        "reltol": 1e-9,
        "abstol": 1e-9,
        "expect": {"signals": ["capacitor1.v"]}
      }
    }
  }
}
end

Test Cases

using ElectricalComponents
using DyadInterface: TransientAnalysis, rebuild_sol, ODEAlg
using ModelingToolkit: toggle_namespacing, get_initial_conditions, @named
using CSV, DataFrames, Plots

snapshotsdir = joinpath(dirname(dirname(pathof(ElectricalComponents))), "test", "snapshots")

<< @setup-block not executed in draft mode >>

Test Case case1

@named model_case1 = ElectricalComponents.Analog.Examples.ChuaCircuit()
model_case1 = toggle_namespacing(model_case1, false)

model_case1 = toggle_namespacing(model_case1, true)
result_case1 = TransientAnalysis(; model = model_case1, alg = ODEAlg.Auto(), start = 0e+0, stop = 2e+2, abstol=1e-9, reltol=1e-9)
sol_case1 = rebuild_sol(result_case1)

<< @setup-block not executed in draft mode >>

df_case1 = DataFrame(:t => sol_case1[:t], :actual => sol_case1[model_case1.capacitor1.v])
dfr_case1 = try CSV.read(joinpath(snapshotsdir, "ElectricalComponents.Analog.Examples.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 >>

plt

<< @example-block not executed in draft mode >>

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