Supporting Information S3
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چکیده
Supporting Information S3. Mathematical analysis of difference equations of axon growth The monotonic growth of axons along the longitudinal direction In some particular cases the dynamical behaviour of solutions of system (main text Eq. 4) can be studied analytically to highlight certain important features of growing axons. In particular, it will provide a useful comparison between the generation of biologically realistic axons and the behaviour of the underlying difference equations. This Section provides a qualitative analysis for two simplified versions of the axon growth model. Reduction of the axon growth model to a one-dimensional map. Let us assume that the dorso-ventral gradient and the random variable are absent and the rostro-caudal gradient is constant as well. With these assumptions the axon growth model (main text Eq. 4) is simplified to the following equations:
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