  Typically, the period-doubling bifurcations exhibited by nonlinear
dissipative systems are observed when varying systems' parameters. In contrast,
the period-doubling bifurcations considered in the current research are induced
by changing the initial conditions whereas parameter values are fixed. Thus,
the studied bifurcations can be classified as the period-doubling bifurcations
without parameters. Moreover, we show a cascade of the period-doubling
bifurcations without parameters resulting in transition to deterministic chaos.
The explored effects are demonstrated by means of numerical modelling on an
example of a modified Anishchenko-Astakhov self-oscillator where the ability to
exhibit bifurcations without parameters is associated with the properties of a
memristor. Finally, we compare the dynamics of the ideal-memristor-based
oscillator with the behaviour of a model taking into account the memristor
forgetting effect.
