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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... 

This paper introduces a fractional order system which can generate regular oscillations or create chaos. It shows that this system is capable to create regular or nonregular oscillations under suitable conditions. These necessary conditions are achieved by violation of the no-chaos criteria. The effective dimension of the proposed system can be chosen any order less than three. Therefore, this system is a good example for limit cycle or chaos generation via fractional-order systems with low orders. Numerical simulations illustrate behavior of the proposed system in different situations. © 2008 Springer Science+Business Media B.V