Models / Lotka-Volterra

Lotka Volterra model

The Lotka-Volterra equations, developed in the 1920s by Alfred Lotka and Vito Volterra representing the cyclic, phase-shifted population dynamics between a predator and its prey.

Diagram of the Lotka-Volterra predator-prey model: prey growth, predation, and predator mortality rates between prey and predator population densities
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Simulation parameters

Alpha 0.1
Beta 0.02
Gamma 0.4
Delta 0.02
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Initial conditions

Prey 10
Predator 10
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Analyses

Short Simulation

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Extended Simulation

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Model Details

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Generated LaTeX Code

\begin{align*}
  \frac{d Prey}{dt} &= \alpha \cdot Prey - \beta \cdot Predator \cdot Prey \\ 
  \frac{d Predator}{dt} &= \delta \cdot Predator \cdot Prey - \gamma \cdot Predator
\end{align*}

Fit to data

Fit settings

SettingValue
Fit backend
Function evaluations per progress update
Maximum total function evaluations
Stop once residual norm reaches
Curriculum learning (advanced)

Every bar shares one fixed step budget. Drag a divider to move a cutoff, drag a bar's top edge (or focus it and use the arrow keys) to change its share — the final stage isn't draggable, it always gets whatever's left. Double-click a bar or use its + to split it, use a divider's × (or Delete/Backspace while it's focused) to remove it.

Split into equal stages:
min viable
1000 it. (final)
t=0 t=100
StageData cutoffIteration budget
1 (final)full data1000 iterations (runs to convergence within this)

Data

Plot options

ParameterFitLog-spaceInitial guess / fixed value Fitted value
Alpha —
Beta —
Gamma —
Delta —

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