Calculus
Lab: systems, trajectories and equilibria
Two quantities changing together: follow a point in the plane and read both time curves. Tap the plane to choose new initial data.
Equations and initial data
One second between advances. Each advance covers 1/100 of interval T, not necessarily one model time unit. Use the slider to select an instant.
Phase plane: x horizontal, y vertical
Tap the plane to change (x₀,y₀) within the allowed limits, then press Play. The system stays the same; the plot adapts its scale to the trajectory.
Both quantities over time
Gray arrows show direction, not speed: they are normalized. The gray point is the initial state. The teal line is the trajectory up to the orange point. Dashed lines are nullclines: x′=0 (teal) and y′=0 (orange); an equilibrium is a common point.
Values at the selected time
Value table
The plot is exploration, not proof or an ecological forecast. Classification near zero determinant or discriminant depends on numerical tolerances. Edited coefficients define the actual system: the preset name no longer guarantees its type.