`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_{N R} (v_{C 1}) = G b \cdot v_{C 1} + \frac{1}{2} (G a - G b) (| v_{C 1} + V e | - | v_{C 1} - V e |)

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

c a p a c i t o r 1. C \cdot \frac{d (v_{C 1})}{d t} = c o n d u c t o r . G \cdot (v_{C 2} - v_{C 1}) - i_{N R} (v_{C 1})

c a p a c i t o r 2. C \cdot \frac{d (v_{C 2})}{d t} = c o n d u c t o r . G \cdot (v_{C 1} - v_{C 2}) - i_{L}

i n d u c t o r . L \cdot \frac{d (i_{L})}{d t} = v_{C 2} - r e s i s t o r . 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.ChuaCircuit()

Behavior

[\begin{matrix} connect (i n d u c t o r_{+} n, r e s i s t o r_{+} p) \\ connect (i n d u c t o r_{+} p, c a p a c i t o r 2_{+} p, c o n d u c t o r_{+} p) \\ connect (c o n d u c t o r_{+} n, n o n l i n e a r_{r e s i s t o r_{+} p}, c a p a c i t o r 1_{+} p) \\ connect (g r o u n d_{+} g, r e s i s t o r_{+} n, c a p a c i t o r 2_{+} n, c a p a c i t o r 1_{+} n, n o n l i n e a r_{r e s i s t o r_{+} n}) \\ inductor . v (t) = - inductor . n . v (t) + inductor . p . v (t) \\ inductor . i (t) = inductor . p . i (t) \\ inductor . p . i (t) + inductor . n . i (t) = 0 \\ inductor . L \frac{d inductor . i (t)}{d t} = inductor . v (t) \\ resistor . v (t) = - resistor . n . v (t) + resistor . p . v (t) \\ resistor . i (t) = resistor . p . i (t) \\ resistor . p . i (t) + resistor . n . i (t) = 0 \\ resistor . v (t) = resistor . R resistor . i (t) \\ conductor . v (t) = conductor . p . v (t) - conductor . n . v (t) \\ conductor . i (t) = conductor . p . i (t) \\ conductor . p . i (t) + conductor . n . i (t) = 0 \\ conductor . i (t) = conductor . G conductor . v (t) \\ capacitor 1. v (t) = - capacitor 1. n . v (t) + capacitor 1. p . v (t) \\ capacitor 1. i (t) = capacitor 1. p . i (t) \\ capacitor 1. n . i (t) + capacitor 1. p . i (t) = 0 \\ capacitor 1. C \frac{d capacitor 1. v (t)}{d t} = capacitor 1. i (t) \\ capacitor 2. v (t) = capacitor 2. p . v (t) - capacitor 2. n . v (t) \\ capacitor 2. i (t) = capacitor 2. p . i (t) \\ capacitor 2. n . i (t) + capacitor 2. p . i (t) = 0 \\ capacitor 2. C \frac{d capacitor 2. v (t)}{d t} = capacitor 2. i (t) \\ nonlinear_resistor . v (t) = nonlinear_resistor . p . v (t) - nonlinear_resistor . n . v (t) \\ nonlinear_resistor . i (t) = nonlinear_resistor . p . i (t) \\ nonlinear_resistor . n . i (t) + nonlinear_resistor . p . i (t) = 0 \\ nonlinear_resistor . i (t) = i f e l s e (nonlinear_resistor . v (t) < - nonlinear_resistor . Ve, - nonlinear_resistor . Ga nonlinear_resistor . Ve + nonlinear_resistor . Gb (nonlinear_resistor . Ve + nonlinear_resistor . v (t)), i f e l s e (nonlinear_resistor . v (t) > nonlinear_resistor . Ve, nonlinear_resistor . Ga nonlinear_resistor . Ve + nonlinear_resistor . Gb (- nonlinear_resistor . Ve + nonlinear_resistor . v (t)), nonlinear_resistor . Ga nonlinear_resistor . v (t))) \\ ground . g . v (t) = 0 \end{matrix}]

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"]}}}}
}
end

Flattened 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"]}}}}
}
end

Test Cases

Test Case `case1`

julia

plt

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ChuaCircuit ​

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Test Case case1 ​

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`ChuaCircuit`

Usage

Behavior

Source

Test Cases

Test Case `case1`

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