Dynamical System Simulator

Dynamical System Simulator is the interactive tool for visualizing differential equations in real time. Watch animated particles flow through 2D and 3D space, tracing their paths as they evolve according to first-order and second-order systems. Perfect for students and researchers who need to verify slope fields, construct phase portraits, and develop intuitive understanding of complex dynamical behavior.

Explore a rich library of pre-loaded systems spanning classic configurations: from one-dimensional models like Logistic Population and Periodic Harvesting, to two-dimensional dynamics including Saddles, Sources, Sinks, and Spiral behaviors, through to three-dimensional phenomena like the famous Lorenz attractor and bifurcations. Each system can be customized with randomized parameters to discover new behaviors and deepen your grasp of how initial conditions shape long-term dynamics.

Tailor every aspect of your simulation to suit your learning goals. Switch between Matrix mode for linear systems and Expressions mode for nonlinear analysis. Control particle count, simulation speed, and time scale—including reverse time integration to trace backward trajectories. Customize visualization with adjustable line width and color, pinch-to-zoom navigation, and full 3D view rotation. Define custom systems using mathematical expressions with support for variables (x, y, z, and their derivatives in second-order mode), time-dependent terms, and a complete set of trigonometric and mathematical functions.

The app assumes knowledge of differential equations but includes a help screen pointing to additional learning resources. Whether you're verifying theoretical predictions, exploring bifurcation behavior, or gaining intuition about equilibria and stability, Dynamical System Simulator provides the interactive visualization environment you need. The application is open source, enabling the community to contribute improvements and new features. Dynamical System Simulator transforms abstract equations into tangible, observable motion—making the invisible dynamics of nonlinear systems visible and understandable.