2021/09/28 by Cenk Demir, Demir, Cenk, Shumon Koga +3
Mathematics · Biochemistry, Genetics and Molecular Biology · #Mathematical Biology Tumor Growth #Microtubule and mitosis dynamics #Cellular Mechanics and Interactions
paper · pdf · doi:10.48550/arxiv.2109.14095
In this work, stabilization of an axonal growth in a neuron associated with\nthe dynamics of tubulin concentration is proposed by designing a boundary\ncontrol. The dynamics are given by a parabolic Partial Differential Equation\n(PDE) of the tubulin concentration, with a spatial domain of the axon's length\ngoverned by an Ordinary Differential Equation (ODE) coupled with the tubulin\nconcentration in the growth cone. We propose a novel backstepping method for\nthe coupled PDE-ODE dynamics with a moving boundary, and design a control law\nfor the tubulin concentration flux in the soma. Through employing the Lyapunov\nanalysis to a nonlinear target system, we prove a local exponential stability\nof the closed-loop system under the proposed control law in the spatial\nH1-norm.\n