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Analysis of Multiplicative Differential Equation Systems with Constant Coefficients: Solutions and Stability | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 خرداد 1405 اصل مقاله (1 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2026.72083.3631 | ||
| نویسنده | ||
| Inass Abdulkadir khaleele* | ||
| University of technology, Baghdad | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Multiplicative derivative؛ Dynamical systems؛ Existence of solution؛ Exponential matrix | ||
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آمار تعداد مشاهده مقاله: 10 تعداد دریافت فایل اصل مقاله: 6 |
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