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

作　　者：Roseline Ngozi Okereke Sadik Olaniyi Maliki Roseline Ngozi Okereke;Sadik Olaniyi Maliki(Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria)

机构地区：[1]Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Nigeria

出　　处：《Applied Mathematics》2016年第18期2324-2335,共12页应用数学（英文）

摘　　要：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.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.

关 键 词：Phase Portrait Trajectory Flow HOMEOMORPHISM Asymptotic Stability MATHCAD 

分 类 号：O17[理学—数学]