Study points of rest hereditarity dynamic systems Van der Pol-Duffing

Using numerical modeling, oscillograms and phase trajectories were constructed to study the limit cycles of a van der Pol-Duffing nonlinear oscillatory system with a power memory. The simulation results showed that in the absence of a power memory ($\alpha=2$, $\beta=1$) or the classical van der Pol Duffing dynamical system, there is a single stable limit cycle, i.e. Lienar theorem holds. In the case of viscous friction ($\alpha=2$, $0<\beta<1$), there is a family of stable limit cycles of various shapes. In other cases, the limit cycle is destroyed in two scenarios: a Hopf bifurcation (limit cycle-limit point) or (limit cycle-aperiodic process). Further continuation of the research may be related to the construction of the spectrum of Lyapunov maximal exponents in order to identify chaotic oscillatory regimes for the considered hereditary dynamic system (HDS).