On the nonlinear features of time-delayed feedback oscillators (Q1877580)

The authors are developing new approaches to determine bifurcations in systems of equations with delay. The main tool is the mode analysis. Two examples are considered \[ \dot x(t)=\delta x(t-\tau) -\varepsilon x^3 (t-\tau),\qquad \text{ and } \] \[ \ddot x + \omega_0^2 x -\alpha_1 \dot x +\alpha_2 \dot x^3 = k \cos (\Omega t) + \beta_1 [ \dot x(t-\tau)-\dot x(t)] + \beta_2 [\dot x(t-\tau)-\dot x(t)]^3, \] where all parameters are positive.