Dynamical analysis of a discrete conformable fractional order bacteria population model in a microcosm

Guven Kaya, Senol Kartal and Fuat Gurcan

Physica A: Statistical Mechanics and its Applications, 2020, vol. 547, issue C

Abstract: In this paper, conformable fractional order differential equations with piecewise constant arguments are used for a modeling population density of a bacteria species in a microcosm. The discretization process of a differential equation with piecewise constant arguments gives us two dimensional discrete dynamical system in the interval t∈[nh,(n+1)h). By using the center manifold theorem and the bifurcation theory, it is shown that the discrete dynamical system undergoes flip and Neimark–Sacker bifurcation depending on the parameter r. It is observed that the model describes some biological phenomena for a bacteria population such as homogeneous bacteria distributions and inhomogeneous spatial population distributions. In addition, the effect of fractional order derivative on dynamic behavior of the system is investigated. Finally, all theoretical results are supported by numerical simulations.

Keywords: Conformable fractional derivative; Piecewise constant arguments; Stability; Flip and Neimark–Sacker bifurcation (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:547:y:2020:i:c:s0378437119321478

DOI: 10.1016/j.physa.2019.123864

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