Analysis of Multiplicative Differential Equation Systems with Constant Coefficients: Solutions and Stability

Articles in Press

Document Type : Research Paper

Author

University of technology, Baghdad

Abstract

In this paper, we study the first-order system of multiplicative differential equations with constant coefficients. The multiplicative differential equations model the rate of change in relation to the quantity itself, while the standard additive differential equations cannot model this type of phenomenon or need more complicated calculations. In this paper we present some new results about the first-order system of multiplicative differential equations with constant coefficients like presenting an explicit closed-form solution formula based on matrix exponentiation; necessary and sufficient conditions for the asymptotic stability of the equilibrium solution $Y \equiv \mathbf{1}$; a characterization of periodic solutions in terms of purely imaginary eigenvalues; and a Lyapunov-type theorem for exponential stability. Examples are presented to demonstrate the efficiency of our findings.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 15 June 2026

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History

  • Receive Date: 23 April 2026
  • Revise Date: 25 May 2026
  • Accept Date: 03 June 2026

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