1403.7554Mar 28, 201420 pages, published in 2015 in Nonlinear Differential Equations and Applications

Stability tests for second order linear and nonlinear delayed models

Leonid Berezansky, Elena Braverman, Lev Idels

Abstract

For the nonlinear second order Lienard-type equations with time-varying delays $\ddot{x}(t)+\sum_{k=1}^m f_k(t,x(t),\dot{x}(g_k(t)))+\sum_{k=1}^l s_k(t,x(h_k(t)))=0,$

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For the nonlinear second order Lienard-type equations with time-varying delays x(t)+∑_k=1^m f_k(t,x(t),x(g_k(t)))+∑_k=1^l s_k(t,x(h_k(t)))=0, global asymptotic stability conditions are obtained. The results are based on the new sufficient stability conditions for relevant linear equations and are applied to derive explicit stability conditions for the nonlinear Kaldor-Kalecki business cycle model.

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The paper addresses: Stability tests for second order linear and nonlinear delayed models.
For the nonlinear second order Lienard-type equations with time-varying delays x(t)+∑_k=1^m f_k(t,x(t),x(g_k(t)))+∑_k=1^l s_k(t,x(h_k(t)))=0, global asymptotic stability conditions are obtained.

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Author comment: 20 pages, published in 2015 in Nonlinear Differential Equations and Applications

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