Synchronous dynamics of a delayed two-coupled oscillator

Abstract

This paper presents a detailed analysis on the dynamics of a delayed two-coupled oscillator. Linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. By means of the equivariant Hopf bifurcation theorem, we not only investigate the effect of time delay on the spatio-temporal patterns of periodic solutions emanating from the trivial equilibrium, but also derive the formula to determine the direction and stability of Hopf bifurcation. Moreover, we illustrate our results by numerical simulations.

Keywords

• periodic solution
• hopf bifurcation
• stability