Exploration on dynamics in a discrete predator–prey competitive model involving feedback controls

Abstract

In this work, we set up a new discrete predator–prey competitive model with time-varying delays and feedback controls. By virtue of the difference inequality knowledge, a sufficient condition which guarantees the permanence of the established discrete predator–prey competitive model with time-varying delays and feedback controls is derived. Under some appropriate parameter conditions, we have proved that the periodic solution of the system without delay exists and globally attractive. To verify the correctness of the derived theoretical fruits, we give two examples and execute computer simulations. Our obtained results are novel and complement previous known results.

Keywords:

• Competitive model
• permanence
• feedback control
• delay
• global attractivity

Mathematics Subject Classification (2000):

• 34K20
• 34C25
• 92D25

Data availability statement

No data were used to support this study.

Disclosure statement

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

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant numbers 12261015, 62062018], Project of High-level Innovative Talents of Guizhou Province [grant number [2016]5651], Guizhou Key Laboratory of Big Data Statistical Analysis [grant number [2019]5103], Key Project of Hunan Education Department [grant number 17A181], University Science and Technology Top Talents Project of Guizhou Province [grant number KY[2018]047], Foundation of Science and Technology of Guizhou Province [grant number [2019]1051], Guizhou University of Finance and Economics [grant number 2018XZD01].