Geodesic
Study points of rest hereditarity dynamic systems Van der Pol-Duffing
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 26 (2019) no. 1, pp. 71-77

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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 ($\alpha=2$, $0\beta1$), 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).
Keywords: limit cycle, exponential Van der Pol-Duffing oscillator, Hopf bifurcation,  oscillograms and phase trajectories. 
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     author = {E. R. Novikov{\cyra} and R. I. Parovik},
     title = {Study points of rest hereditarity dynamic systems {Van} der {Pol-Duffing}},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
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E. R. Novikovа; R. I. Parovik. Study points of rest hereditarity dynamic systems Van der Pol-Duffing. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 26 (2019) no. 1, pp. 71-77. http://geodesic.mathdoc.fr/item/VKAM_2019_26_1_a6/