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Asymptotically periodic solutions of fractional order systems with applications to population models

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  • He, Hua
  • Wang, Wendi

Abstract

Motivated by applications in population models, we consider S-asymptotically periodic solution of fractional differential equations with periodic environment forces or asymptotically periodic ones. The system is quasi-monotone, and the existence of positive S-asymptotically periodic solution is established by using upper and lower solutions. The sufficient conditions that ensure the uniqueness of positive S-asymptotically periodic solution are also established on the basis of theory of sublinear operator. The applications of the general conclusions to classical population models yield the global convergence of positive S-asymptotically periodic solution in logistic equation with or without weak Allee effect, and the model of two cooperative populations.

Suggested Citation

  • He, Hua & Wang, Wendi, 2024. "Asymptotically periodic solutions of fractional order systems with applications to population models," Applied Mathematics and Computation, Elsevier, vol. 476(C).
    • Handle: RePEc:eee:apmaco:v:476:y:2024:i:c:s0096300324002297
    DOI: 10.1016/j.amc.2024.128760
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