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This study uses a thermistor as a physical memristor in a chaotic circuit. The research reveals a novel route to Shilnikov spiral chaos, resulting in a unique double spiral attractor.

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Area of Science:

  • Nonlinear dynamics
  • Circuit theory
  • Chaos theory

Background:

  • Leon Chua's 1976 work modeled thermistors as memristive devices.
  • Memristor emulators are commonly used in chaotic systems.
  • Physical memristors offer potential advantages over emulators.

Purpose of the Study:

  • To utilize a thermistor as a physical memristor in a Muthuswamy-Chua chaotic circuit.
  • To investigate the dynamical properties of a circuit incorporating a thermistor-based memristor.
  • To explore novel routes to chaos and attractor formation.

Main Methods:

  • Designed a circuit with a linear inductor, linear capacitor, nonlinear resistor, and a thermistor (nonlinear memristor).
  • Modeled the circuit using a new three-dimensional autonomous dynamical system.
  • Performed mathematical analysis and numerical simulations.

Main Results:

  • The circuit exhibits a transition from torus breakdown to chaos.
  • This transition follows the route to Shilnikov spiral chaos.
  • A unique "double spiral attractor" was observed.

Conclusions:

  • A thermistor can effectively function as a physical memristor in chaotic circuits.
  • The proposed system demonstrates a novel route to chaos with a double spiral attractor.
  • This research contributes to understanding memristor-based chaotic dynamics.