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Dynamical System Simulator Screenshot 1
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About Dynamical System Simulator

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)

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Frequently Asked Questions(FAQ)

What is Dynamical System Simulator?

Dynamical System Simulator is a software that animates 2D and 3D systems of differential equations in real time, allowing users to observe and gain intuition about dynamical systems.

What can I do with Dynamical System Simulator?

With Dynamical System Simulator, you can watch animated particles moving through space, leaving trails behind them. It is useful for verifying slope fields, phase portraits, and understanding dynamical systems intuitively.

Do I need knowledge of differential equations to use Dynamical System Simulator?

Yes, knowledge of differential equations is assumed to make the most of Dynamical System Simulator. However, the app provides help and additional sources of information to assist users.

What sample systems are pre-loaded in Dynamical System Simulator?

Some of the pre-loaded systems in Dynamical System Simulator include Logistic Population, Periodic Harvesting, Saddle, Source, Sink, Center, Spiral Source, Spiral Sink, Bifurcations, Homoclinic Orbit, Spiral Saddle, Lorenz, and Oscillations.

What are the mode settings available in Dynamical System Simulator?

The mode settings in Dynamical System Simulator include Matrix (linear) or Expressions (linear or non-linear), 2D or 3D visualization, and 1st Order or 2nd Order systems.

What simulation settings can be adjusted in Dynamical System Simulator?

Users can adjust the number of particles, update rate, time scale (including negative values), and enable or disable random initial velocities for particles.

What view settings are available in Dynamical System Simulator?

View settings in Dynamical System Simulator include line width, line color, zooming (using pinch gestures), and view rotation (only applicable in 3D mode).

Can I use symbols and trigonometric functions in Expressions Mode?

Yes, in Expressions Mode, you can use symbols such as x, y, z, x', y', z' (2nd Order Mode only), t (time), and trigonometric functions like sin, cos, asin, acos, and abs (absolute value).
author
This app should be more popular.
Yog_G
author
I don't even understand dynamics but this made me enjoy it and no ad spamming i truly enjoy playing this
disappointment
author
So, setting the number of particles to 300 means 300 differential equations. Amazing.
Doug Star
author
🛰️♻️🛰️each*SITE*MINIMIZER📡♻️📲
Nicholas Guerrero
author
it's a great app. Very helpful
prakash borah
author
I have not found another app of this kind like it. Very good. Just one small thing, it would be nice to have an auto rotate feature. This is so cool 🤩 In first order 3D expressions try using these three for...
DOUG Philp