Plotting the bifurcation diagram of a chaotic dynamical system
A chaotic dynamical system is highly sensitive to initial conditions; small perturbations at any given time yield completely different trajectories. The trajectories of a chaotic system tend to have complex and unpredictable behaviors.
Many real-world phenomena are chaotic, particularly those that involve nonlinear interactions among many agents (complex systems). Examples can be found in meteorology, economics, biology, and other disciplines.
In this recipe, we will simulate a famous chaotic system: the logistic map. This is an archetypal example of how chaos can arise from a very simple nonlinear equation. The logistic map models the evolution of a population, taking into account both reproduction and density-dependent mortality (starvation).
We will draw the system's bifurcation diagram, which shows the possible long-term behaviors (equilibria, fixed points, periodic orbits, and chaotic trajectories) as a function of the...
