Stability tests for second order linear and nonlinear delayed models
  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. 
Leonid Berezansky, Elena Braverman and Lev Idels
math.DS