Stability tests for second order linear and nonlinear delayed models

Leonid Berezansky; Elena Braverman; Lev Idels

Stability tests for second order linear and nonlinear delayed models

Dynamical Systems 2016-06-13 v2

Authors: Leonid Berezansky , Elena Braverman , Lev Idels

Abstract

For the nonlinear second order Lienard-type equations with time-varying delays $\ddot{x}(t)+\sum_{k=1}^m f_k(t,x(t),\dot{x}(g_k(t)))+\sum_{k=1}^l s_k(t,x(h_k(t)))=0,$ 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. We also explore multistability of the sunflower non-autonomous equation and its modifications.

Keywords

delay differential equations stability analysis stability theory

Cite

@article{arxiv.1403.7554,
  title  = {Stability tests for second order linear and nonlinear delayed models},
  author = {Leonid Berezansky and Elena Braverman and Lev Idels},
  journal= {arXiv preprint arXiv:1403.7554},
  year   = {2016}
}

Comments

20 pages, published in 2015 in Nonlinear Differential Equations and Applications

Stability tests for second order linear and nonlinear delayed models

Abstract

Keywords

Cite

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