Phase Diagrams and Bifurcation Diagrams of Logistic Map with Code Implementation

This program package consists of five distinct computational sections. The first two sections implement logistic map visualizations: the phase diagram displays system behavior across different parameter values using iterative population growth equations (x_n+1 = rx_n(1-x_n)), while the bifurcation diagram tracks sudden behavioral transitions as parameter r varies from 2.4 to 4.0, revealing period-doubling routes to chaos. Sections three through five focus on henon map analysis (x_n+1 = 1 - ax_n² + y_n, y_n+1 = bx_n), featuring phase space trajectories, bifurcation patterns with parameter a variation, and a comparative plot juxtaposing henon and logistic map behaviors using normalized metrics. The code employs matrix operations for efficient iteration, scatter plots for phase visualization, and Lyapunov exponent calculations to quantify chaotic characteristics. Through these computational experiments, researchers can deeply explore dynamic system behaviors and observe fascinating phenomena like attractor formation and sensitivity to initial conditions across parameter spaces.