Existence of chaos in the fractional order unified system: The lowest effective dimension

This paper deals with the existence of chaos in the fractional order unified system. In an earlier published work, based on the numerical simulation results it is claimed that the lowest effective dimension in the fractional order unified system in order to present chaotic behaviors is 2.76. In this paper, it is analytically shown that the fractional order unified system can be chaotic for effective dimensions lower than the claimed lowest effective dimension. Also, the lowest effective dimension for existence of chaos in such a system is analytically determined. Computer simulation results, obtained based on a reliable numerical method, are brought to back up the presented analytical work in the paper.