Asymptotic Behaviour of Solutions of Certain Third Order Nonlinear Differential Equations via Phase Portrait AnalysisReport as inadecuate




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The global phase portrait describes thequalitative behaviour of the solution set for all time. In general, this is asclose as we can get to solving nonlinear systems. The question of particularinterest is: For what parameter values does the global phase portrait of adynamical system change its qualitative structure? In this paper, we attempt toanswer the above question specifically for the case of certain third ordernonlinear differential equations of the form . The linear case where  is alsoconsidered. Our phase portrait analysis shows that under certain conditions onthe coefficients as well as the function , we have asymptotic stability ofsolutions.

KEYWORDS

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

Cite this paper

Okereke, R. and Maliki, S. 2016 Asymptotic Behaviour of Solutions of Certain Third Order Nonlinear Differential Equations via Phase Portrait Analysis. Applied Mathematics, 7, 2324-2335. doi: 10.4236-am.2016.718183.





Author: Roseline Ngozi Okereke, Sadik Olaniyi Maliki

Source: http://www.scirp.org/



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