Bifurcations in a delay logistic equation under small perturbations (Q2027819)

Consider the following equation, known as the delay logistic equation, \[ \frac{du}{dt}=\lambda \big[ 1-u(t-T)\big] u \quad (\lambda >0, \ T>0), \] which is encountered in mathematical ecology, physics, etc. In the first part of the paper, the local behavior of solutions to the above equation is analyzed by using bifurcation methods. In particular, the author studies the dependence of dynamic properties of solutions on small perturbations of the above equation that contain a large delay \(h>0\). The second part of the paper is devoted to the delay logistic equation with periodic perturbations of parameters. Using standard asymptotic methods the parametric resonance is deduced under a two-frequency perturbation.