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Simulate and Visualize Verbal Theories as Differential Equations
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Define Your Target System
Number of Variables
Univariate
Bivariate
Type of Model
Linear ODE
Polynomial ODE
Linear SDE (OU Model)
Polynomial SDE
Harmonic Oscillator (Undamped) ODE
Damped Oscillator ODE
Harmonic Oscillator (Undamped) SDE
Damped Oscillator SDE
Define Parameters
Name: Mean/Intercept
Range: (-∞, +∞)
μ
Name: Auto-Effect
Range: (-∞, 0]
β
Name: Linear Auto-Effect
Range: (-∞, 0]
β
1
Name: Quadratic Auto-Effect
Range: (-∞, 0]
β
2
Name: Cubic Auto-Effect
Range: (-∞, 0]
β
3
Name: Bi-quadratic Auto-Effect
Range: (-∞, 0]
β
4
Name: Frequency
Range: (-∞, 0]
ω
Name: Damping
Range: (-∞, +∞)
ζ
Name: White Noise Scaling SD
Range: [0, +∞)
σ
Name: Initial Value of y at time t
0
Range: (-∞, +∞)
y
0
Reset Parameters
Name: Seed for Random Number Generator
Range: {1, 2, ...}
Set Your Seed
Choose a Random Seed
Define Time
Use the slider to choose the time period of simulation: (t
0
, T)
Time Period
Name: Time Step
Choose an appropriate time step to iterate the process in the specified Time Period.
Δt
Equation of the System
Plot of Y Over Time
Loading...
Generate Plot
Variable X
Type of model
Linear ODE
Linear SDE (OU Model)
Harmonic Oscillator (Undamped) ODE
Damped Oscillator ODE
Harmonic Oscillator (Undamped) SDE
Damped Oscillator SDE
Define Parameters of X
Name: Mean of X
Range: (-∞, +∞)
μ
x
Name: Auto-Effect of X
Range: (-∞, 0]
β
x
Name: Frequency of X
Range: (-∞, 0]
ω
x
Name: Coupling Effect of Y on X
Range: (-∞, +∞)
γ
x
Name: damping of X
Range: (-∞, +∞)
ζ
x
Name: White Noise Scaling SD of X
Range: [0, +∞)
σ
x
Name: Initial Value of X at time t
0
Range: (-∞, +∞)
x
0
Reset X's Parameters
Variable Y
Type of model
Linear ODE
Linear SDE (OU Model)
Harmonic Oscillator (Undamped) ODE
Damped Oscillator ODE
Harmonic Oscillator (Undamped) SDE
Damped Oscillator SDE
Define Parameters of Y
Name: Mean of Y
Range: (-∞, +∞)
μ
y
Name: Auto-Effect of Y
Range: (-∞, 0]
β
y
Name: Frequency of Y
Range: (-∞, 0]
ω
y
Name: Coupling Effect of X on Y
Range: (-∞, +∞)
γ
y
Name: damping of Y
Range: (-∞, +∞)
ζ
y
Name: White Noise Scaling SD of Y
Range: [0, +∞)
σ
y
Name: Initial Value of Y at time t
0
Range: (-∞, +∞)
y
0
Reset Y's Parameters
Name: Seed for Random Number Generator
Range: {1, 2, ...}
Set Your Seed
Choose a Random Seed
Define Time
Use the slider to choose the time period of simulation: (t
0
, T)
Time Period
Name: Time Step
Choose an appropriate time step to iterate the process in the specified Time Period.
Δt
Define the Coupling Between X and Y
Variable-Centered Coupling
Mean-Centered Coupling
Equation of the System
Plot of X and Y Over Time
Loading...
Generate Plot