Figure 2: The chaotic trajectory of system (5.12). of Li-Yorke is provided for DETS, and the ingredients of the Li-Yorke chaos, proximality and frequent separation, are theoretically proved. The results can be used to obtain chaotic mechanical systems and electrical circuits on time scales without any restriction in the dimension. The authors wish to express their sincere gratitude to the referees for the helpful criticism and valuable suggestions, which helped to improve the paper significantly. The second author is supported by the 2219 scholarship programme of TÜBİTAK, the Scientific and Technological Research Council of Turkey. −0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 −0.125 −0.085 −0.045 −0.005 0.035 0.075 y$_{1}$ y 2 Acknowledgments References [1] Akhmet, M. U. & Turan, M. [2006] “The differential equations on time scales through impulsive differential equations,” Nonlinear Analysis $_{65}$, 2043–2060. [2] Akhmet, M. U. & Turan, M. [2009] “Differential equations on variable time scales,” Nonlinear Analysis $_{70}$, 1175–1192. [3] Akhmet, M. U. [2009a] “Devaney’s chaos of a relay system,” Commun. Nonlinear Sci. Numer. Simulat. $_{14}$, 1486–1493. [4] Akhmet, M. U. [2009b] “Li-Yorke chaos in the impact system,” J. Math. Anal. Appl. $_{351}$, 804–810. [5] Akhmet, M. U. [2009c] “Dynamical synthesis of quasi-minimal sets,” Int. J. Bifurcation and Chaos $_{19}$, 2423–2427. [6] Akhmet, M. [2010] Principles of Discontinuous Dynamical Systems , (Springer, New York). 13