Periodic Solutions of Kolmogorov Systems on Quantum Time Scales

Abstract

Kolmogorov systems are one of the important models in applied mathematics which are used for modelling various biological processes. In the present work, we concentrate on the coupled functional dynamic equations as Kolmogorov systems on quantum time scales and study the existence of their periodic solutions. As it is well-known, quantum time scales are not translation invariant, and this results in using multiplicative periodicity perceptions as an alternative to conventional periodicity. In the presentation of the main outcomes, we focus on Kolmogorov systems with/without delay term and we employ coincidence degree theory and fixed point theory for investigating the sufficient conditions for the existence of positive periodic solutions. This research provides an alternative approach to the related literature since it turns the spotlight on Kolmogorov models constructed on non-translation invariant time domains and serves a better understanding for the complicated dynamics of Kolmogorov systems involving periodic structures.