On the vector Lyapunov Functions and Asymptotic Eventual Stability for nonlinear Impulsive Differential Equations via Comparison Principle

Authors

  • Dodi Kanu Igobi Department of Mathematics, University of Uyo, Uyo Author
  • Jeremiah Ugeh Atsu Department of Mathematics, University of Cross River State, Calabar Author
  • Jackson Efiong Ante Department of Mathematics, Topfaith University, Mkpatak, Nigeria; Author
  • Joseph Oboyi Department of Mathematics, University of Calabar, Calabar; Author
  • Udeme Emmanuel Ebere Department of Mathematics/Computer Science, Ritman University, Ikot Ekpene, Nigeria Author
  • Emmanuel Emmanuel Asuk Department of Mathematics, University of Cross River State, Calabar; Author
  • Paul Edet Okon Department of Electrical/Electronics, Topfaith University, Mkpatak, Nigeria Author
  • Samuel Okon Essang Department of Mathematics, Arthur Jarvis University, Akpabuyo, Nigeria Author
  • Uwem Prospero Akai Department of Mathematics, Topfaith University, Mkpatak, Nigeria Author
  • Emmanuel Francis Runyi Department of Statistics, Federal Polytechnic, Ugep, Nigeria Author
  • Godwin Odido Igomah Department of Physics, University of Calabar, Calabar, Nigeria Author
  • Benedict Iserom Ita Department of Mathematics, University of Uyo, Uyo Author

DOI:

https://doi.org/10.60787/jnamp.vol69no1.459

Keywords:

Electrical conductivity., Correlation analysis, Electromagnetic induction, Environmental monitoring, ShapeMetal detection

Abstract

In this paper, the asymptotic eventual stability of nonlinear impulsive differential equations with fixed moments of impulse is examined using the vector Lyapunov functions, which is generalized by a class of piecewise continuous Lyapunov functions. The novelty in the use of the vector Lypunov functions lies in the fact that the "restrictions" encountered by the scalar Lyapunov function is safely handled especially for large scale dynamical systems, since the method involves splitting the Lyapunov functions into components so that each of the components can easily describe the behavior of the solution state. Together with comparison results, sufficient conditions for the asymptotic eventual stability are presented.

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Published

2025-03-03

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Vol. 69 No. 1 (2025): February

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How to Cite

On the vector Lyapunov Functions and Asymptotic Eventual Stability for nonlinear Impulsive Differential Equations via Comparison Principle. (2025). The Journals of the Nigerian Association of Mathematical Physics, 69(1), 57-73. https://doi.org/10.60787/jnamp.vol69no1.459

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