Logistic Map Bifurcation Diagram Implementation

This program generates a Logistic Map bifurcation diagram, revealing behavior patterns that differ significantly from typical nonlinear systems. The mathematical mapping is defined by the recurrence relation: xₙ = 1 - a·xₙ₋₁², where a is a real parameter in the interval [0,2]. Key implementation aspects include: - Parameter sweeping through a-values with fine resolution - Transient elimination by iterating initial conditions before recording data - Bifurcation point visualization using scatter plots - Chaotic regime detection through Lyapunov exponent calculations For deeper understanding of the underlying theory and applications, refer to these resources: - "Chaos: Making a New Science" by James Gleick (Chinese translation by Xu Mingda et al., Shanghai Science and Technology Press, 1991) - "Nonlinear Dynamics and Chaos" by Steven Strogatz (Chinese translation by Wei Yunfeng et al., Science Press, 2009) - "Introduction to Nonlinear Science" by H. Stokes (Chinese translation by Yang Hongzhi et al., People's Posts and Telecommunications Press, 2001) The code efficiently handles large iteration counts using vectorization techniques and includes optional features for zooming into specific parameter regions and calculating fractal dimensions.