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Ogbu, H.M., Okereke, R.N. and Aliyu, B.Y. (2012) The Three Equivalent First Order Systems of a Third Order Scalar Equation and Its Application on Stability of Solutions of Ordinary Differential Equations. IJAPS, 4.

has been cited by the following article:

• TITLE: Asymptotic Behaviour of Solutions of Certain Third Order Nonlinear Differential Equations via Phase Portrait Analysis

  AUTHORS: Roseline Ngozi Okereke, Sadik Olaniyi Maliki

  KEYWORDS: Phase Portrait, Trajectory, Flow, Homeomorphism, Asymptotic Stability, MathCAD

  JOURNAL NAME: Applied Mathematics, Vol.7 No.18, December 14, 2016

  ABSTRACT: The global phase portrait describes the qualitative behaviour of the solution set for all time. In general, this is as close as we can get to solving nonlinear systems. The question of particular interest is: For what parameter values does the global phase portrait of a dynamical system change its qualitative structure? In this paper, we attempt to answer the above question specifically for the case of certain third order nonlinear differential equations of the form . The linear case where is also considered. Our phase portrait analysis shows that under certain conditions on the coefficients as well as the function , we have asymptotic stability of solutions.