Dynamics and thermodynamics of delayed population growth

The dynamic and thermodynamic properties of delayed nonlinear reaction-diffusion equations describing population growth with memory are analyzed. In the dynamic study we first apply the speed selection mechanisms for wave fronts connecting two steady states obtaining, on one hand, a decrease in the lower bound speed, and also an upper bound velocity; we also calculate an exact wave front solution. in the thermodynamic study. we show an agreement between the stochastic description and extended irreversible thermodynamics in the presence of a source of particles.