Loopa: Nonlinear Dynamics (loopa) Package name

Dive into the fascinating world of non-linear dynamics and chaos theory. This simulator provides an interactive environment to explore mathematical models and observe how small changes in parameters lead to vastly different outcomes.

• 90+ continuous systems: Lorenz, Rössler, Chen, Aizawa, Lü, the full Sprott family, hyperchaotic 4D attractors, Duffing, Van der Pol, FitzHugh-Nagumo, Hindmarsh-Rose, Lotka-Volterra, Chua Circuit, double pendulum, and more

• 35+ discrete maps: Logistic, Hénon, Tent, Standard, Gauss, Sine, Circle, Lozi, Ikeda, Tinkerbell, Baker, Bogdanov, Kaplan-Yorke, Zaslavskii, Arnold cat map, and more with cobweb diagram visualization

• Phase space visualization in 2D and 3D with nullclines, flow field, and speed coloring

• Analysis suite: bifurcation diagram, Lyapunov exponents and spectrum with the Kaplan–Yorke dimension, 0–1 test for chaos, recurrence plot, basin of attraction, power spectrum, sensitivity to initial conditions, stable and unstable manifolds, orbit diagram

• Periodic orbits, equilibrium continuation with limit cycles, and two-parameter planes

• Multiple simulation slots for parallel exploration and side-by-side comparison

• Lua scripting to automate simulations and analyses

• Custom system editor for user-defined equations

• Export to SVG, PDF, PNG, and CSV

Loopa is free to try with the Lorenz attractor in 2D and 3D phase space. Unlock all of Loopa with a one-time purchase. No subscription, no ads.