We report, in this paper, a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical solutions revealing several chaotic phenomena such as antimonotonicity, period-doubling sequences and Feignbaum remerging have been presented. Further, the analytical solutions are used to obtain basins of attraction, phase portraits and Poincare maps for different chaotic systems. Experimentally observed chaotic attractors in some of the systems are presented to confirm the analytical results. The bifurcations andchaotic phenomena studied through explicit analytical solutions are reported in the literature for the first time.