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This study reveals period-doubling bifurcations without parameter changes, triggered by initial conditions. This leads to deterministic chaos in a memristor-based oscillator, offering new insights into nonlinear dynamics.

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Area of Science:

  • Nonlinear dynamics and chaos theory.
  • Memristor-based circuit analysis.
  • Bifurcation theory.

Background:

  • Nonlinear dissipative systems typically exhibit period-doubling bifurcations by altering system parameters.
  • Understanding bifurcations is crucial for predicting system behavior and transitions to chaos.

Purpose of the Study:

  • To investigate period-doubling bifurcations induced by initial conditions, independent of parameter variations.
  • To demonstrate a cascade of these parameter-free bifurcations leading to deterministic chaos.
  • To analyze the role of memristors in enabling parameter-free bifurcations.

Main Methods:

  • Numerical modeling of a modified Anishchenko-Astakhov self-oscillator.
  • Investigating bifurcations triggered by changes in initial conditions.
  • Comparing ideal memristor dynamics with a model incorporating memristor forgetting effects.

Main Results:

  • Demonstration of period-doubling bifurcations without parameter changes.
  • Observation of a cascade of bifurcations leading to deterministic chaos.
  • Identification of memristor properties as key to enabling parameter-free bifurcations.

Conclusions:

  • Parameter-free bifurcations, initiated by initial conditions, can induce deterministic chaos.
  • Memristor-based oscillators offer a novel platform for studying these unique bifurcations.
  • The memristor forgetting effect influences the dynamics of the oscillator.