The topical problem of making the robust sources of chaotic signals is considered. Using of such sources is quite necessary аt working out of modem systems of information transmission, store and processing. Obviously, it must be precise devices, i.e. devices with stable statistical properties regarding to variations of their parameters, and it must be realised sufficiently simply in practice. In this connection both problems of study
of modified logistic map dynamics and of comparing given mathematical model with the real physical system are formulated and solved. 
The borders and attraction basin of the time series attractor generated by the тар were determined. The values of order parameters separating regular, chaotic and strictly chaotic types of motion were found. Analytical expressions for calculating the Kolmogorov entropy and Shannon information entropy were obtained. It was shown, that while generating chaotic motion the order parameter’s behaviour corresponds with the
second order phase transition. The roughness of the appearing attractor was discovered. Relation between the map being investigated and the physical system with delayed feedback and with infinite phase space dimension was proved. Obtained results make the prospect for application of the modified logistic map as a basis for operation of the chaotic oscillations sources which can be realised in an analogous and numerical form.