arXiv subjects

Sabrina Streipert

Publications and source records attributed to Sabrina Streipert.

3 recordsLinked to original sources

arXiv2026

Phase Plane Analysis on Time Scales for a Lotka-Volterra Competition Model

In this work, we formulate a two-species Lotka--Volterra competition model on time scales. To derive the global dynamics of solutions of this planar model, we introduce a dynamic augmented phase plane analysis that extends the traditional phase plane analysis known to be a powerful tool in the analysis of planar differential equations. In the case of a constant graininess, the method is consistent with the augmented phase portrait introduced for the discrete space. However, for non-constant graininess, this augmented phase plane is time-dependent and therefore dynamic. Despite the dynamic character, we are able to identify time-independent information that allows the conclusion of the global dynamics of the introduced Lotka--Volterra competition model on time scales. The dynamic phase plane method, albeit only introduced in the context of this particular two-species competition model, it can be extended to other planar systems on time scales, providing a novel technique to study the global dynamics of planar systems on time scales.

math.DS↗

arXiv2020

Square Root Laws in Structured Fisheries

We introduce the term net-proliferation in the context of fisheries and establish relations between the proliferation and net-proliferation that are economically and sustainably favored. The resulting square root laws are analytically derived for species following the Beverton-Holt recurrence but, we show, can also serve as reference points for other models. The practical relevance of these analytically derived square root laws is tested on the the Barramundi fishery in the Southern Gulf of Carpentaria, Australia. A Beverton-Holt model, including stochasticity to account for model uncertainty, is fitted to a time series of catch and abundance index for this fishery. Simulations show, that despite the stochasticity, the population levels remain sustainable under the square root law. The application, with its inherited model uncertainty, sparks a risk sensitivity analysis regarding the probability of populations falling below an unsustainable threshold. Characterization of such sensitivity helps in the understanding of both dangers of overfishing and potential remedies.

q-bio.PE↗

arXiv2018

Exact Solution to a Dynamic SIR Model

We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's approach. If the coefficients are constant, both solution methods yield the same result. After a brief introduction to time scales, we formulate the SIR (susceptible-infected-removed) model in the general time domain and derive its solution. In the discrete case, this provides the solution to a new discrete epidemic system, which exhibits the same behavior as the continuous model. The last part is dedicated to the analysis of the limiting behavior of susceptible, infected, and removed, which contains biological relevance.

math.CA↗