ABSTRACT
A population growth is modeled as a special example, and has been afforded by the nonlinear difference equation called the logistic map. Particularly, for onedimensional chaotic maps, a bifurcation diagram of the two-parameter quadratic family has been observed, and the self-adjusting logistic map with a slowly changing parameter in time has been considered. For onedimensional chaotic maps, a bifurcation diagram of the two-parameter quadratic family has been observed, and the self-adjusting logistic map with a slowly changing parameter in time has been considered. Chaotic and fractal dynamics have been expanded to experimental observations with the mathematical models, and fractal compression has been presented to compress images using fractals. A two-dimensional (2D) chaotic map and the fractal set are considered for the physical analog of snow crystal, and the nonlinear dynamics on the fractal set are discussed by iterating the 2D map.
