<p>This study examines the stability and boundedness properties of solutions for a system of nonlinear vector delay differential equations (VDDEs) by establishing the conditions under which the solutions are stable and ultimately bounded as <i>t</i> → ∞. The method used is yapunov-Krasovskii’s (L–K), which involves constructing a continuous scalar function related to the differential equations describing the system’s dynamics and delay effects. A numerical example with geometrical arguments illustrates the effectiveness of the results obtained. These findings significantly improve upon those in existing literature and the impact of this study reaches beyond theoretical (VDDEs), influencing diverse areas such as control theory, population dynamics, and neurobiology, where systems may demonstrate delayed reactions to inputs or changes in state. By setting forth sufficient criteria for stability and boundedness, this research offers critical insights for developing and executing control strategies in engineering, forecasting population behaviors in ecology, and comprehending temporal patterns in biological systems.</p>

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Stability and boundedness analysis for a system of nonlinear vector delay differential equations

  • A. L. Olutimo,
  • A. A. Adeyanju,
  • I. F. Ogbu,
  • S. A. Iyase

摘要

This study examines the stability and boundedness properties of solutions for a system of nonlinear vector delay differential equations (VDDEs) by establishing the conditions under which the solutions are stable and ultimately bounded as t → ∞. The method used is yapunov-Krasovskii’s (L–K), which involves constructing a continuous scalar function related to the differential equations describing the system’s dynamics and delay effects. A numerical example with geometrical arguments illustrates the effectiveness of the results obtained. These findings significantly improve upon those in existing literature and the impact of this study reaches beyond theoretical (VDDEs), influencing diverse areas such as control theory, population dynamics, and neurobiology, where systems may demonstrate delayed reactions to inputs or changes in state. By setting forth sufficient criteria for stability and boundedness, this research offers critical insights for developing and executing control strategies in engineering, forecasting population behaviors in ecology, and comprehending temporal patterns in biological systems.