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In this paper, we study some chaotic properties of s-dimensional dynamical system of the form Ψ(a1, a2, . . . , as)  (gs(as), g1(a1), . . . , gs−1(as−1)), where ak ∈ Hk for any k ∈ 1, 2, . . . , s { }, s≥ 2 is an integer, and Hk is a compact subinterval of the real lineR  (−∞, +∞) for any k ∈ 1, 2, . . . , s { }. Particularly, a necessary and sufficient condition for a cyclic permutation map Ψ(a1, a2, . . . , as)  (gs(as), g1(a1), . . . , gs−1(as−1)) to be LY-chaotic or h-chaotic or RT-chaotic or D-chaotic is obtained. Moreover, the LY-chaoticity, h-chaoticity, RT-chaoticity, and D-chaoticity of such a cyclic permutation map is explored. Also, we proved that the topological entropy h(Ψ) of such a cyclic permutationmap is the same as the topological entropy of each of the following maps: gj ∘ gj−1 ∘ · · · ∘g1l ∘gs ∘gs−1 ∘ · · · ∘gj+1, if j  1, . . . , s − 1and gs ∘gs−1 ∘ · · · ∘g1, and thatΨ is sensitive if and only if at least one of the coordinates maps of Ψ is sensitive.

The Topological Entropy of Cyclic Permutation Maps and Some Chaotic Properties on Their MPE sets