Dynamical System Simulator

Simplicial Software, LLC

About this app

Dynamical System Simulator animates 2D and 3D first-order and second-order systems of differential equations in real time. Watch animated particles move through space leaving a trail in their wake. Great for verifying slope fields, phase portraits, and gaining an intuitive understanding of dynamical systems. Knowledge of differential equations is assumed but the help screen will point you to additional sources of information. The app is pre-loaded with several well known dynamical system configurations that can be selected from the navigation drawer. Parameters for a particular system type can be randomized.


Sample Systems:
• Logistic Population (1D)
• Periodic Harvesting (1D)
• Saddle (2D)
• Source (2D)
• Sink (2D)
• Center (2D)
• Spiral Source (2D)
• Spiral Sink (2D)
• Bifurcations (2D)
• Homoclinic Orbit (2D)
• Spiral Saddle (3D)
• Spiral Sink (3D)
• Lorenz (3D)
• Oscillations (3D)


Mode Settings:
• Matrix (linear) / Expressions (linear or non-linear)
• 2D / 3D
• 1st Order / 2nd Order


Simulation Settings:
• Number of Particles
• Update Rate
• Time Scale (including negative)
• Enable/Disable random initial velocities for particles


View Settings:
• Line Width
• Line Color
• Zooming (with pinch gestures)
• View Rotation (3D only)


In Expressions Mode the following symbols and trigonometric functions can be used:
• x, y, z
• x', y', z' (2nd Order Mode Only)
• t (time)
• sin (sine)
• cos (cosine)
• asin (arcsine)
• acos (arccosine)
• abs (absolute value)


This application was recently made open source for the benefit of students and other users of the software. Feel free to submit PRs with new features or bug fixes at https://github.com/simplicialsoftware/systems

Ratings and reviews

Thx for fixing the app!!!! Awesome support!!! on once again y'all really sat here and remove the time how you remove the time Don't make no sense Where's the timer at the top left the top right I mean I don't know what iteration I'm at.

Really fun app. I think it'd be nice to have more control over a particle's initial conditions though, and maybe the ability to simply graph one at said initial conditions instead of watching it over time. Excellent work though regardless.

Simply amazing with excellence.Plz add pause-button to stop running while source-equation edited and screen cleared for a new shot.One thing confusing though: two equations with two variables,each second-order,makes a fourth-order system in each of variables in reality;so,the system-order labeling in the app isn't strictly correct.

What's new

- Library updates
- Reduce CPU utilization
- Dynamical System Simulator is now open source: https://github.com/simplicialsoftware/systems