Budworm: a Streamlit App

Module 1: Low-Dimensional Dynamics

With the functions from Budworm: the Model in Code and Budworm: Integration and Time Series, you can build an interactive app in which a slider changes a parameter and the plots update immediately. See the Streamlit documentation.

Setup

Streamlit runs on your own machine, not in Google Colab. Follow the instructions in the README of the course repository to set up your environment.

Create a script spruce_budworm_app.py. Either import your functions from a module (for example spruce_budworm_model.py) or paste them into the script. A separate module is better practice. Run the app with

streamlit run spruce_budworm_app.py

Sidebar controls

Create sliders for:

• growth rate \(r\) (range 0.0 to 1.0, default 0.5);
• carrying capacity \(k\) (range 0.1 to 10.0, default 10.0);
• time to evolve (range 1 to 100, default 10).

Set the initial population to \(x_0 = k/10\).

Interactive features

• Display the differential equation with the current parameter values.
• Show the rate plot from the rate plot section and the time series from the time series section.
• Add an “Evolve” button that continues the simulation and updates the plots.
• Store the time and population arrays in st.session_state. Streamlit reruns the whole script on every interaction, so anything not stored there is reset.

Layout

import numpy as np
import streamlit as st

from your_module import (
    evolve_spruce_budworm,
    plot_spruce_budworm,
    plot_spruce_budworm_rate,
)

st.title("Spruce Budworm Population Dynamics")

r = st.sidebar.slider("Intrinsic growth rate (r)", 0.0, 1.0, 0.5)
k = st.sidebar.slider("Carrying capacity (k)", 0.1, 10.0, 10.0)
x0 = k / 10

# Initialize session state on the first run
if "sbw_x" not in st.session_state:
    st.session_state["sbw_t"] = np.array([0.0])
    st.session_state["sbw_x"] = np.array([x0])

t_eval = st.sidebar.slider("Time", 1, 100, 10)
button = st.sidebar.button("Evolve")

t = st.session_state["sbw_t"]
x = st.session_state["sbw_x"]

if button:
    t, x = evolve_spruce_budworm(t, x, r=r, k=k, t_eval=t_eval)
    st.session_state["sbw_t"] = t
    st.session_state["sbw_x"] = x

fig1, ax1 = plot_spruce_budworm_rate(x[-1], r=r, k=k)
st.pyplot(fig1)
fig2, ax2 = plot_spruce_budworm(t, x)
st.pyplot(fig2)

Validation

• With \(r = 0.5\), \(k = 10\) and \(x_0 = 1\), pressing “Evolve” several times should bring the population to about 0.68.
• The green line on the rate plot should always sit where the time series ends.

Optional extension

• Add a reset button that clears st.session_state.
• Show several trajectories with different initial conditions.
• Animate the population dynamics.
• Let \(k\) drift slowly in time and plot \(x\) against \(k\) to see the hysteresis loop of Hysteresis.

A complete reference app is in the streamlit folder of the repository.

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