Some criteria of chaos in non-autonomous discrete dynamical systems

References

• J.S. Cánovas, Li–Yorke chaos in a class of non-autonomous discrete systems, J. Differ. Equ. Appl. 17 (2011), pp. 479–486. doi: 10.1080/10236190903049025
   Web of Science ®Google Scholar
• Q. Huang, Y. Shi, and L. Zhang, Sensitivity of non-autonomous discrete dynamical systems, Appl. Math. Lett. 39 (2015), pp. 31–34. doi: 10.1016/j.aml.2014.08.007
   Web of Science ®Google Scholar
• H. Ju, H. Shao, Y. Choe, and Y. Shi, Conditions for maps to be topologically conjugate or semi-conjugate to subshifts of finite type and criteria of chaos, Dyn. Syst. 31 (2016), pp. 496–505. doi: 10.1080/14689367.2016.1158240
   Web of Science ®Google Scholar
• H. Ju, C. Kim, Y. Choe, and M. Chen, Conditions for topologically semi-conjugacy of the induced systems to the subshift of finite type, Chaos Solitons Fractals 98 (2017), pp. 1–6. doi: 10.1016/j.chaos.2017.02.012
   Web of Science ®Google Scholar
• J. Kennedy and J.A. Yorke, Topological horseshoes, Trans. Am. Math. Soc. 353 (2001), pp. 2513–2531. doi: 10.1090/S0002-9947-01-02586-7
   Web of Science ®Google Scholar
• C. Kim, H. Ju, M. Chen, and P. Raith, A-Coupled-expanding and distributional chaos, Chaos Solitons Fractals 77 (2015), pp. 291–295. doi: 10.1016/j.chaos.2015.06.010
   Web of Science ®Google Scholar
• S. Kolyada and L. Snoha, Topological entropy of non-autonomous dynamical systems, Random Comput. Dyn. 4 (1996), pp. 205–233.
   Google Scholar
• M. Kulczycki and P. Oprocha, Coupled-expanding maps and matrix shifts, Internat. J. Bifur. Chaos23 (2013), pp. 1–6. doi: 10.1142/S0218127413500132
   Web of Science ®Google Scholar
• C. Robinson, Dynamical Systems: Stability Symbolic Dynamics and Chaos, 2nd ed., CRC Press, Florida, 1999.
   Google Scholar
• H. Shao, Y. Shi, and H. Zhu, Strong Li–Yorke chaos for time-varying discrete systems with A-coupled-expansion, Internat. J. Bifur. Chaos 25 (2015), pp. 1550186. (10 p). doi: 10.1142/S0218127415501862
   Web of Science ®Google Scholar
• H. Shao, Y. Shi, and H. Zhu, Lyapunov exponents, sensitivity, and stability for non-autonomous discrete systems, Internat. J. Bifur. Chaos 28 (2018), pp. 1850088. (7 p). doi: 10.1142/S0218127418500888
   Web of Science ®Google Scholar
• H. Shao, Y. Shi, and H. Zhu, On distributional chaos in non-autonomous discrete systems, Chaos Solitons Fractals 107 (2018), pp. 234–243. doi: 10.1016/j.chaos.2018.01.005
   Web of Science ®Google Scholar
• Y. Shi, Chaos in non-autonomous discrete dynamical systems approached by their induced systems, Internat. J. Bifur. Chaos 22 (2012), pp. 1250284. (12 p).
   Web of Science ®Google Scholar
• Y. Shi and G. Chen, Chaos of discrete dynamical systems in complete metric spaces, Chaos Solitons Fractals 22 (2004), pp. 555–571. doi: 10.1016/j.chaos.2004.02.015
   Web of Science ®Google Scholar
• Y. Shi and G. Chen, Chaos of time-varying discrete dynamical systems, J. Differ. Equ. Appl. 15 (2009), pp. 429–449. doi: 10.1080/10236190802020879
   Web of Science ®Google Scholar
• Y. Shi, H. Ju and G. Chen, Coupled-expanding maps and one-sided symbolic dynamical systems, Chaos Solitons Fractals 39 (2009), pp. 2138–2149. doi: 10.1016/j.chaos.2007.06.090
   Web of Science ®Google Scholar
• C. Tian and G. Chen, Chaos of a sequence of maps in a metric space, Chaos Solitons Fractals 28 (2006), pp. 1067–1075. doi: 10.1016/j.chaos.2005.08.127
   Web of Science ®Google Scholar
• L. Wang, G. Liao, and Y. Yang, Recurrent point set of the shift on Σ and strong chaos, Ann. Polon. Math. LXX VIII 2 (2002), pp. 124–130.
   Google Scholar
• X. Wu and P. Zhu, Chaos in a class of non-autonomous discrete systems, Appl. Math. Lett. 26 (2013), pp. 431–436. doi: 10.1016/j.aml.2012.11.003
   Web of Science ®Google Scholar
• X. Yang and Y. Tang, Horseshoes in piecewise continuous maps, Chaos Solitons Fractals 19 (2004), pp. 841–845. doi: 10.1016/S0960-0779(03)00202-9
   Web of Science ®Google Scholar
• X. Zhang and Y. Shi, Coupled-expanding maps for irreducible transition matrices, Int. J. Bifurcat. Chaos 20 (2010), pp. 3769–3783. doi: 10.1142/S0218127410028094
   Web of Science ®Google Scholar
• X. Zhang, Y. Shi, and G. Chen, Some properties of coupled-expanding maps in compact sets, Proc. Am. Math. Soc. 141 (2013), pp. 585–595. doi: 10.1090/S0002-9939-2012-11339-5
   Web of Science ®Google Scholar
• L. Zhang, Y. Shi, H. Shao, and Q. Huang, Chaos induced by weak A-coupled-expansion of non-autonomous discrete dynamical systems, J. Differ. Equ. Appl. 22 (2016), pp. 1747–1759. doi: 10.1080/10236198.2016.1243104
   Web of Science ®Google Scholar
• Z. Zhou, Symbolic Dynamics, Shanghai Scientific and Technological Education Publishing House, Shanghai, 1997.
   Google Scholar
• Y. Zhu, Z. Liu, X. Xu, and W. Zhang, Entropy of non-autonomous dynamical systems, J. Korean Math. Soc. 49 (2012), pp. 165–185. doi: 10.4134/JKMS.2012.49.1.165
   Web of Science ®Google Scholar
• H. Zhu, Y. Shi, and H. Shao, Devaney chaos in nonautonomous discrete systems, Internat. J. Bifur. Chaos 26 (2016), pp. 1650190. (10 p).
   Web of Science ®Google Scholar