Effect of immigration in a predator-prey system: Stability, bifurcation and chaos

KANGALGİL F., IŞIK S.

AIMS MATHEMATICS, cilt.7, sa.8, ss.14354-14375, 2022 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 7 Sayı: 8
  • Basım Tarihi: 2022
  • Doi Numarası: 10.3934/math.2022791
  • Dergi Adı: AIMS MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Social Sciences Citation Index (SSCI), Scopus, Directory of Open Access Journals
  • Sayfa Sayıları: ss.14354-14375
  • Anahtar Kelimeler: predator-prey system, fixed point, stability, immigration, Neimark-Sacker bifurcation, flip bifurcation, chaotic behavior, OGY feedback control method, NEIMARK-SACKER BIFURCATION, COMPLEX DYNAMICS, MODEL
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

In the present manuscript, a discrete-time predator-prey system with prey immigration is considered. The existence of the possible fixed points of the system and topological classification of coexistence fixed point are analyzed. Moreover, the existence and the direction for both NeimarkSacker bifurcation and flip bifurcation are investigated by applying bifurcation theory. In order to control chaos due to the emergence of the Neimark-Sacker bifurcation, an OGY feedback control strategy is implemented. Furthermore, some numerical simulations, including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the system, are given to support the accuracy of the analytical finding. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behavior in the system.