Chaos induced by weak A-coupled-expansion of non-autonomous discrete dynamical systems

Abstract

This paper focuses on chaos induced by weak A-coupled-expansion of non-autonomous discrete systems in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, separately. A new concept of weak A-coupled-expansion for non-autonomous discrete systems, whose condition is weaker than that of A-coupled-expansion, is introduced, and several new criteria of chaos induced by weak A-coupled-expansion of non-autonomous discrete systems are established. By applying some close relationships between chaotic dynamical behaviours of the original system and its induced systems, two criteria of chaos are established. One example is provided for illustration.

Keywords:

• Chaos
• non-autonomous discrete system
• weak coupled-expansion
• coupled-expansion

AMS Subject Classifications:

• 37B55
• 37D45
• 37B10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the NNSF of China [grant number 11571202]; the Young and Middle-Aged Scientists Research Awards Foundation of Shangdong Province, China [grant number BS2013SF029]; A Project of Shandong Province Higher Educational Science and Technology Program, China [grant number J15LI04]; the Research Foundation for Advanced Talents of Ludong University, China [grant number LY2012015].