A review on phase plane and non-linear system of differential equations with application

Authors

  • Asnake Tadese Abtew Deneba high school
  • Tesfaye Tefra Mamo Debre Berhan University

Keywords:

Phase portrait, Phase trajectory, Closed orbit, Separatrix, Eigenvalues, Linearization

Abstract

In this paper we review on nonlinear phenomena and properties, particularly those with physical relevance. Often, mathematical models of real-world phenomena are formulated in terms of systems of nonlinear differential equations, which may be difficult to solve explicitly. Finding a solution to a differential equation may not be so important if that solution never appears in the physical model represented by the system, or is only realized in exceptional circumstances. Thus, equilibrium solutions, which correspond to configurations in which the physical system does not move, only occur in everyday situations if they are stable. An unstable equilibrium will not appear in practice, since slight perturbations in the system or its physical surroundings will immediately dislodge the system far away from equilibrium. We take a qualitative approach to the analysis of solutions to nonlinear systems by making phase portraits and using stability analysis.

Author Biographies

Asnake Tadese Abtew, Deneba high school

Amhara Region, North Shoa Zone, Department of mathematics, Deneba high school, Deneba, Ethiopia

Tesfaye Tefra Mamo, Debre Berhan University

College of Natural and Computational Science, Department of Mathematics, Debre Berhan University, Ethiopia

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Published

2021-06-30

How to Cite

Asnake Tadese Abtew, & Tesfaye Tefra Mamo. (2021). A review on phase plane and non-linear system of differential equations with application. Berhan International Research Journal of Science and Humanities, 5(1), 155–165. Retrieved from http://journals.dbu.edu.et/index.php/birjsh/article/view/90