Cobweb Explorer
Visualize the long-term behavior of discrete-time models. Adjust the growth rate r and watch stable fixed points give way to period-doubling cycles and chaos. Includes a dual-orbit mode for exploring sensitive dependence on initial conditions.
Launch →Bifurcation Explorer
See the full picture at once. Click anywhere on the bifurcation diagram to set r and watch the cobweb and time series update instantly — from stable fixed points through period-doubling all the way to chaos.
Launch →Loggerhead Turtle Simulator
A real, published stage-structured population model for an endangered species. Adjust survival at each life stage and watch the dominant eigenvalue — and the population's fate — respond, exactly as in the original conservation study.
Launch →Difference equations · cobwebbing · fixed points and stability
The Ricker model · continuous-time models and the phase line · Euler's method · replicator dynamics
Harvesting and bifurcation in continuous models · structured populations, projection matrices, and eigenvalues
In 1987, a seven-stage population matrix for the endangered loggerhead sea turtle showed that decades of effort protecting eggs on nesting beaches could never have saved the species — the population's growth rate was far more sensitive to survival of juveniles at sea. That single finding helped drive adoption of Turtle Excluder Devices in shrimp trawls. Explore the actual model in the Loggerhead Turtle Simulator above.