The effect of quadrature on the dynamics of a discretized nonlinear integro-differential equation (Q1964382)

The integro-differential equation of population dynamics \[ \phi'(t)=\phi(t)\left(1-\int_{-\infty}^tK(t-\tau)\phi(\tau)d\tau\right), \enskip t>0 \] with convolution kernel is studied. The Euler approximation implies a discrete model. The existence and stability of fixed and periodic points are investigated. The analysis of spurious periodic solutions and numerical results are given. In conclusion an adaptive algorithm based on local error control is developed.