Stability tests for second order linear and nonlinear delayed models

  • Leonid Berezansky
  • Elena Braverman
  • Lev IdelsEmail author


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

Mathematics Subject Classification

34K20 92D25 34K45 34K12 34K25 


Second order delay differential equations Global asymptotic stability Boundedness of solutions Lienard-type nonautonomous linear and nonlinear delay differential equations Sunflower equation The Kaldor–Kalecki business cycle model Variable delays 


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© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsBen-Gurion University of the NegevBeer ShevaIsrael
  2. 2.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  3. 3.Department of MathematicsVancouver Island UniversityNanaimoCanada

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