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

• 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 ${mx^2}/{((A+x)(B+x))}$] and some other monotone functions, has always at least one $\omega$-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].
Mathematics Subject Classification: Primary: 34C25, 39A11; Secondary: 39A12, 92D25.

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