In the current paper the dynamics of a mixed parabolic-gradient system is examined. Thesystem, which is a coupled system of parabolic equations and gradient equations, acts as a first model for the outgrowth of axons in a developing nervous system. For modeling considerations it is relevant to know the influence of the parameters in the system and the source profiles in the parabolic equations on the dynamics. These subjects are discussed together with an approximation which uses the quasi-steady-state solutions of the parabolic equations instead of the parabolic equations themselves. Some of the findings are demonstrated by numerical simulations.

None of the above, but in MSC2010 section 70Kxx (msc 70K99), Diffusion processes (msc 60J60), Initial value problems (msc 65L05), Neural biology (msc 92C20)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

Krottje, J.K. (2002). On the dynamics of a mixed parabolic-gradient system. Modelling, Analysis and Simulation [MAS]. CWI.