Global dynamics of a state-dependent delay model with unimodal feedback (Q1931543)

The differential system \[ x'(t) =-\mu x(t) +b(x(t-\tau(t))), \tau'(t) = h(x(t), \tau(t)) \] with state-dependent delay is considered, where \(\mu > 0\), \(x\), \(h\) and \(b\) are real-valued differentiable functions and \(b\) is unimodal on \([0, +\infty)\) with certain properties. Aiming at finding the asymptotic behaviour of the system, the authors obtain a series of results on existence and uniqueness, global convergence as \(t\to +\infty\), global attraction of a positive stationary state, and Hopf bifurcation when the stationary state loses its global attractivity. This is a fruitful continuation of one of the author's previous works.