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Periodic solutions for a semi-ratio-dependent predator-prey dynamical system with a class of functional responses on time scales

Mostafa, F ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.3934/dcdsb.2008.9.267
  3. Publisher: 2008
  4. Abstract:
  5. In this paper we explore the existence of periodic solutions of a nonautonomous semi-ratio-dependent predator-prey dynamical system with functional responses on time scales. To illustrate the utility of this work, we should mention that, in our results this system with a large class of monotone functional responses, always has at least one periodic solution. For instance, this system with some celebrated functional responses such as Holling type-II (or Michaelis-Menten), Holling type-III, Ivlev, mx (Holling type I), sigmoidal [e.g., Real and mx2/((A + x)(B +x))] and some other monotone functions, has always at least one ω-periodic solution. Besides, for some well-known functional responses which are not monotone such as Monod-Haldane or Holling type-IV, the existence of periodic solutions is proved. Our results extend and improve previous results presented in [4], [10], [22] and [38]
  6. Keywords:
  7. Periodic solution ; Nonautonomous predator-prey system ; Dynamical system on time scales ; Coincidence degree ; Functional response
  8. Source: Discrete and Continuous Dynamical Systems - Series B ; Volume 9, Issue 2 , 2008 , Pages 267-279 ; 15313492 (ISSN)
  9. URL: https://www.aimsciences.org/article/doi/10.3934/dcdsb.2008.9.267