Impulse Effect on the Food-Limited Population Model with Piecewise Constant Argument

KARAKOÇ F.

APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, cilt.15, sa.2, ss.957-969, 2020 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 2
  • Basım Tarihi: 2020
  • Dergi Adı: APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.957-969
  • Anahtar Kelimeler: Food-limited population model, Piecewise constant argument, Impulse, Difference equation, Linearized oscillation, DIFFERENTIAL-EQUATIONS, ASYMPTOTIC-BEHAVIOR, GLOBAL ATTRACTIVITY, OSCILLATION
  • Ankara Üniversitesi Adresli: Evet

Özet

The qualitative study of mathematical models is an important area in applied mathematics. In this paper, a version of the food-limited population model with piecewise constant argument under impulse effect is investigated. Differential equations with piecewise constant arguments are related to difference equations. First, a representation for the solutions of the food-limited population model is stated in terms of the solutions of corresponding difference equation. Then using linearized oscillation theory for difference equations, a sufficient condition for the oscillation of the solutions about positive equilibrium point is obtained. Moreover, asymptotic behavior of the non-oscillatory solutions are investigated. Later, applying the same theory, non-impulsive model is also studied. Numerical examples are given to compare the results of impulsive model with the results of non-impulsive case. The results show that when the solutions of impulsive differential equation model are oscillatory about positive equilibrium under suitable conditions the solutions of the corresponding non-impulsive model is not oscillatory. This situation indicates to the importance of impulse effects on the asymptotic behavior of the solutions.