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Various differentiable models are frequently used to describe the dynamics of complex systems (see the kinetic models, fluid models etc.). Given the complexity of all the physical phenomena involved in the dynamics of such systems, it is required to introduce the dynamic variables dependences both on the space-time coordinates and on the scale resolutions. Therefore, in this case an adequate theoretical approach may be the use of non-linear physical models in the form, either of the Scale Relativity Theory, or of the Extended Scale Relativity Theory, i.e. the Scale Relativity Theory with an arbitrary constant fractal dimension. In the framework of the Extended Scale Relativity Theory, fractal velocity field is described both by topological solitons of kink type and by non-topological soliton varieties of breather type. Moreover, using a simplified version of the fractal hydrodynamic models, the dynamics of a free Gaussian ‘‘perturbation’’ is analyzed. Applications for the blood flow are proposed. The results revealed the directional flow towards the walls, which can explain the thickening effect which is one of the source of arteriosclerosis.

Non-Linear Behaviours in the Dynamics of Some Biostructures