Share This Article:

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

Full-Text HTML XML Download Download as PDF (Size:890KB) PP. 2324-2335
DOI: 10.4236/am.2016.718183    1,125 Downloads   1,694 Views Citations

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.

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.

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.