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.