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In this paper, we propose to use a linear system with switching methodology for description and analysis of complex biological systems. We show advantages of the proposed approach over the one usually used, which is based on ODE. We propose the detailed methodology of a full analysis of developed models, including analytical determination of the location and type of equilibrium points, finding an analytical solution, stability and bifurcation analysis. We illustrate the above with the example of the well-known p53 signalling pathway compar