Dynamics of a Delay Limit Cycle Oscillator with Self-Feedback

This paper concerns the dynamics of the following nonlinear differential-delay equation:in which T is the delay and is a coefficient of self-feedback. Using numerical integration, continuation programs and bifurcation theory, we show that this system exhibits a wide range of dynamical phenomena, including Hopf and pitchfork bifurcations, limit cycle folds and relaxation oscillations. It is shown that this equation governs the in-phase and out-of-phase motions of a system of two coupled nonlinear differential-delay equations.