The integrated and local estimations of instability for a class of autonomous delay systems

The Lyapunov stability of a partly nonlinear delay system is investigated both analytically and numerically for the sake of calculation of (i) integrated and (ii) local estimates. The improvement of numerical scheme for calculation of characteristic exponents is achieved within the integrated analysis and the properties of mutual similarity of the internal product are proved. At the local instabilities investigation, two kinds of instability for the delay system with high-power nonlinearity are detected. The intermittency of the chaotic behavior is also explored numerically and analogy with hydrodynamic turbulence is shown.