Some criteria of chaos in non-autonomous discrete dynamical systems

ABSTRACT

This paper establishes several criteria for strong Li–Yorke chaos and distributional chaos in non-autonomous discrete dynamical systems. The main criterion of distributional δ-chaos for some $\delta >0$ is induced by weak A-coupled-expansion in a sequence of nonempty compact subsets, where A is an irreducible transition matrix with at least one row sum larger than 1. Some of these results not only extend the existing related results for autonomous discrete systems to non-autonomous discrete systems, but also relax the assumptions of the counterparts. One example of a non-autonomous logistic system is provided for illustration.

Keywords:

• Non-autonomous discrete dynamical system
• strong Li–Yorke chaos
• distributional chaos
• coupled-expansion
• irreducible transition matrix

2010 Mathematics Subject Classifications:

• 37B55
• 37D45
• 37B10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the Hong Kong Research Grants Council [GRF Grant CityU11200317] and the National Natural Science Foundation of China (NNSF of China) [grant number 11571202].