Chaos induced by snap-back repellers in non-autonomous discrete dynamical systems

Abstract

This paper focuses on chaos induced by snap-back repellers in non-autonomous discrete systems. A new concept of snap-back repeller for non-autonomous discrete systems is introduced and several new criteria of chaos induced by snap-back repellers in non-autonomous discrete systems are established. In addition, it is proved that a regular and nondegenerate snap-back repeller in non-autonomous discrete systems implies chaos in the (strong) sense of Li–Yorke. Two illustrative examples are proved.

Keywords:

• Chaos
• snap-back repeller
• non-autonomous discrete system
• weak 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]; a Project of Shandong Province Higher Educational Science and Technology Program, China [grant number J15LI04]; the NSF of Shandong Province, China [grant number ZR2015AM026].