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Chaos is a complex behavior observed in many systems. This book discusses some significant analyses of the logistic equation of the chaotic systems and their behaviors have been studied graphically. In Chapter 1, a brief introduction on chaos is given. Deterministic chaos and the application of chaos theory are also discussed. Chapter 2 gives a comparison of the logistic model and the exponential model. Chapter 3 discusses the logistic equation and the logistic map. In Chapter 4, the bifurcation diagrams are obtained from the logistic equation for different sets of parameters. Chapter 5 is connected with the summary and conclusion of the book. Appendix follows Chapter 5 and Bibliography is given at the end of the book. It has been observed that a small change in initial condition leads a system to chaos; and that sensitivity to initial condition in chaotic systems is verified by the logistic equation and visualized by the bifurcation diagram.