Geodesic
Convergence of Solutions of Third Order Differential Equations*
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 779-792

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Consider a system of differential equations . Solutions of this system are said to be convergent if, given any pair of solutions x(t), y(t), x(t) - y(t) → 0 as t → ∞. In this case the system is also said to be extremely stable.In [6] a technique was developed which yielded the convergence of solutions of the forced Lienard equation. Here a similar technique i s applied to forced third order equations. A critical step in [6] was to show that a certain matrix was negative definite. This could be done directly in [6] since the matrix was only 2 × 2. With third and higher order equations, direct use of necessary and sufficient conditions is not feasible since the computations become unwieldy. 
Swick, K. E. Convergence of Solutions of Third Order Differential Equations*. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 779-792. doi: 10.4153/CMB-1969-101-0
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     author = {Swick, K. E.},
     title = {Convergence of {Solutions} of {Third} {Order} {Differential} {Equations*}},
     journal = {Canadian mathematical bulletin},
     pages = {779--792},
     year = {1969},
     volume = {12},
     number = {6},
     doi = {10.4153/CMB-1969-101-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-101-0/}
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