Qualitative analysis of two systems of nonlinear first-order ordinary differential equations for biological systems

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We consider two systems of nonlinear first-order ordinary differential equations proposed to describe (Formula presented.) -levels in renal vascular smooth muscle cells and in liver cells. Initially, we present the models and its assumptions. We next investigate an approach to local solvability by Picard–Lindelöf 's Theorem. Further, we prove nonnegativity of the systems' possible solutions and we especially conclude global unique existence of the models' solutions by Gronwall-type arguments and the concept of trapping regions. After finishing our theoretical part with some aspects of stability analysis, we provide evidence of our findings by some numerical experiments.


Original languageEnglish
Pages (from-to)4597-4624
Number of pages28
JournalMathematical Methods in the Applied Sciences
Issue number8
Publication statusPublished - 10 Jan 2022

External IDs

unpaywall 10.1002/mma.8056


Research priority areas of TU Dresden

DFG Classification of Subject Areas according to Review Boards

ASJC Scopus subject areas


  • dynamical systems, first-order nonlinear ordinary differential equations, nonnegativity, oscillations, solvability, stability, uniqueness