Interest:

• For which systems does the augmented phase portrait reveal the global dynamics? 

• What is the relation to monotone flows?

Related works:

1. Streipert, S. and Wolkowicz, G. An augmented phase plane approach for discrete planar maps: Introducing next-iterate operators. Mathematical Biosciences, 355, 108924, 2023. link 

2. Streipert, S. and Wolkowicz, G. and Bohner, M. Derivation and Analysis of a Discrete Predator-Prey Model. Bulletin of Mathematical Biology, 84(7): 67, 2022. link 

Interest: 

• Formulation of discrete population models that incorporate a delay in the maturation only. 

• Studying the effect of delay in maturation on a species' survival.

Related works: 

1. Streipert, S. and Wolkowicz, G. S. K. Technique to derive discrete distributed delay population models. Mathematical Biosciences, 376:109279, 2024. link 

2. Streipert, S. and Wolkowicz, G. S. K. Technique to derive discrete population models with delayed growth. Journal of Biological Dynamics (special issue honoring A. Aziz-Yakubu), 17(1): 2244987, 2023.

• Applications of Dynamic Equations on Time Scales

Interest:

Dynamic equations on time scales allows to describe time-dependent processes that change not necessarily discrete nor continuously. It was originally introduced as a unification of the continuous and discrete calculus. I am interested in exploring its potential to real-life processes.

Related works: 

• Bohner, M. and Mesquita, J. and Streipert, S. The Beverton-Holt Model on Isolated Time Scales. Mathematical Biosciences and Engineering, 19 (11): 11693–11716, 2022.

• Bohner, M. and Streipert, S. and Torres, D. Exact solution to a dynamic SIR model. Nonlinear Analysis: Hybrid Systems, 32:228–238, 2019.

• Theory of Dynamic Equations on Time Scales

Interest:

Despite its progress, there are several, largely unexplored areas in the theory of time scales including stability analysis, stochastic dynamical systems, etc. Providing the foundation of such theories on time scales is part of my research. 

Related works:

• Bohner, M. and Mesquita, J. and Streipert, S. Periodic functions on isolated Time Scales. Mathematische Nachrichten, 295(2), 259–280, 2022.

• Bohner, M. and Cuchta, T. and Streipert, S. Delay dynamic equations on isolated time scales and the relevance of one-periodic coefficients. Mathematical Methods in the Applied Sciences, 45(10): 5821–5838, 2022.

Related works: 

1. Wilber, M., DeMarchi, J., Briggs, C. and Streipert, S. Rapid evolution of resistance and tolerance leads to variable host recoveries following disease-induced declines. American Naturalist, 203(5):535-550, 2024. link