ChuaCircuit Icon

`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

ChuaCircuit()

Behavior

\[ \begin{equation} \left[ \begin{array}{c} \mathrm{connect}\left( inductor_{+}n, resistor_{+}p \right) \\ \mathrm{connect}\left( inductor_{+}p, capacitor2_{+}p, conductor_{+}p \right) \\ \mathrm{connect}\left( conductor_{+}n, nonlinear_{resistor_{+}p}, capacitor1_{+}p \right) \\ \mathrm{connect}\left( ground_{+}g, resistor_{+}n, capacitor2_{+}n, capacitor1_{+}n, nonlinear_{resistor_{+}n} \right) \\ \mathtt{inductor.v}\left( t \right) = - \mathtt{inductor.n.v}\left( t \right) + \mathtt{inductor.p.v}\left( t \right) \\ \mathtt{inductor.i}\left( t \right) = \mathtt{inductor.p.i}\left( t \right) \\ \mathtt{inductor.p.i}\left( t \right) + \mathtt{inductor.n.i}\left( t \right) = 0 \\ \mathtt{inductor.L} \frac{\mathrm{d} \mathtt{inductor.i}\left( t \right)}{\mathrm{d}t} = \mathtt{inductor.v}\left( t \right) \\ \mathtt{resistor.v}\left( t \right) = - \mathtt{resistor.n.v}\left( t \right) + \mathtt{resistor.p.v}\left( t \right) \\ \mathtt{resistor.i}\left( t \right) = \mathtt{resistor.p.i}\left( t \right) \\ \mathtt{resistor.p.i}\left( t \right) + \mathtt{resistor.n.i}\left( t \right) = 0 \\ \mathtt{resistor.v}\left( t \right) = \mathtt{resistor.R} \mathtt{resistor.i}\left( t \right) \\ \mathtt{conductor.v}\left( t \right) = \mathtt{conductor.p.v}\left( t \right) - \mathtt{conductor.n.v}\left( t \right) \\ \mathtt{conductor.i}\left( t \right) = \mathtt{conductor.p.i}\left( t \right) \\ \mathtt{conductor.p.i}\left( t \right) + \mathtt{conductor.n.i}\left( t \right) = 0 \\ \mathtt{conductor.i}\left( t \right) = \mathtt{conductor.G} \mathtt{conductor.v}\left( t \right) \\ \mathtt{capacitor1.v}\left( t \right) = - \mathtt{capacitor1.n.v}\left( t \right) + \mathtt{capacitor1.p.v}\left( t \right) \\ \mathtt{capacitor1.i}\left( t \right) = \mathtt{capacitor1.p.i}\left( t \right) \\ \mathtt{capacitor1.n.i}\left( t \right) + \mathtt{capacitor1.p.i}\left( t \right) = 0 \\ \mathtt{capacitor1.C} \frac{\mathrm{d} \mathtt{capacitor1.v}\left( t \right)}{\mathrm{d}t} = \mathtt{capacitor1.i}\left( t \right) \\ \mathtt{capacitor2.v}\left( t \right) = \mathtt{capacitor2.p.v}\left( t \right) - \mathtt{capacitor2.n.v}\left( t \right) \\ \mathtt{capacitor2.i}\left( t \right) = \mathtt{capacitor2.p.i}\left( t \right) \\ \mathtt{capacitor2.n.i}\left( t \right) + \mathtt{capacitor2.p.i}\left( t \right) = 0 \\ \mathtt{capacitor2.C} \frac{\mathrm{d} \mathtt{capacitor2.v}\left( t \right)}{\mathrm{d}t} = \mathtt{capacitor2.i}\left( t \right) \\ \mathtt{nonlinear\_resistor.v}\left( t \right) = \mathtt{nonlinear\_resistor.p.v}\left( t \right) - \mathtt{nonlinear\_resistor.n.v}\left( t \right) \\ \mathtt{nonlinear\_resistor.i}\left( t \right) = \mathtt{nonlinear\_resistor.p.i}\left( t \right) \\ \mathtt{nonlinear\_resistor.n.i}\left( t \right) + \mathtt{nonlinear\_resistor.p.i}\left( t \right) = 0 \\ \mathtt{nonlinear\_resistor.i}\left( t \right) = ifelse\left( \mathtt{nonlinear\_resistor.v}\left( t \right) < - \mathtt{nonlinear\_resistor.Ve}, - \mathtt{nonlinear\_resistor.Ga} \mathtt{nonlinear\_resistor.Ve} + \mathtt{nonlinear\_resistor.Gb} \left( \mathtt{nonlinear\_resistor.Ve} + \mathtt{nonlinear\_resistor.v}\left( t \right) \right), ifelse\left( \mathtt{nonlinear\_resistor.v}\left( t \right) > \mathtt{nonlinear\_resistor.Ve}, \mathtt{nonlinear\_resistor.Ga} \mathtt{nonlinear\_resistor.Ve} + \mathtt{nonlinear\_resistor.Gb} \left( - \mathtt{nonlinear\_resistor.Ve} + \mathtt{nonlinear\_resistor.v}\left( t \right) \right), \mathtt{nonlinear\_resistor.Ga} \mathtt{nonlinear\_resistor.v}\left( t \right) \right) \right) \\ \mathtt{ground.g.v}\left( t \right) = 0 \\ \end{array} \right] \end{equation} \]

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.
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

# 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`

plt

Examples
Experiments
Analyses

ChuaCircuit