Stability analysis in a second-order differential equation with delays

Abstract

A second-order differential equation with finite discrete delays is considered. Local stability of the zero equilibrium is investigated, and we obtain some sufficient conditions for the zero equilibrium is stable or unstable. Moreover, it is found that there exist the local Hopf bifurcations of the system when the delay varies.

Keywords:

• local stability
• discrete delays
• Hopf bifurcation

AMS Subject Classification :

• 34K25
• 39A11