Some aspects of investigation of limit cycles of FitzHugh-Nagumo oscillator with degree memory

In this paper, oscillograms and phase trajectories are constructed using numerical simulation to study the limiting cycles of a nonlinear FitzHugh-Nagumo oscillatory system with power memory. The simulation results showed that in the absence of power memory (α=2, β=1) or the classical dynamic FitzHugh-Nagumo system, there is a single stable limit cycle, i.e. the Lienard theorem is fulfilled. In the case of viscous friction (α=2, 0< β<1), there is a family of stable limit cycles of different shapes. In other cases, the limit cycle destroyed according to two scenarios: 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 maximum Lyapunov exponents for a purpose of identifying chaotic oscillatory regimes for the considered hereditary dynamic system (HDS).