On the population model of the non-autonomous logistic equation of second order with period-two parameters

Abstract

In this paper we study the non-autonomous logistic difference equation

with the nonnegative initial conditions x _− 1, x ₀. In particular, the periodic behavior, the attractivity of solutions and the stability of solutions are discussed in detail.

Keywords:

• Local asymptotic stability
• Invariant interval
• Semicycle behavior
• Global asymptotic stability
• Boundedness

Keywords:

• Primary: 39A10
• 39A11
• Secondary: 47B39

Acknowledgements

The authors are grateful to J. Cushing for his helpful comments. In particular, the explanatory paragraph after system (3.2) and (3.3) is taken from his email. This work was supported by NSERC (Canada) and FQRNT (Québec).

Notes

¹ [email protected]

Additional information

Notes on contributors

Javad Mashreghi

† 1 [email protected]