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A new chaotic oscillator with free control.

Chunbiao Li1, Julien Clinton Sprott2, Akif Akgul3

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This study introduces a novel chaotic system with tunable amplitude, frequency, and offset via a simple linear function modification. This controllable chaotic oscillation is easily implemented in electronic circuits for diverse applications.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Electronic Circuits

Background:

  • Chaotic systems are complex dynamical systems exhibiting sensitive dependence on initial conditions.
  • Existing chaotic oscillators often lack simple methods for independent control of amplitude, frequency, and offset.

Purpose of the Study:

  • To introduce and analyze a novel chaotic system with a unique control mechanism.
  • To demonstrate the feasibility of implementing this system in a practical electronic circuit.

Main Methods:

  • The proposed system incorporates quadratic terms with a single linear function.
  • Mathematical analysis of the system's dynamics and control parameters.
  • Electronic circuit implementation using potentiometers for independent control.

Main Results:

  • The linear function's slope controls amplitude and frequency scaling.
  • The linear function's intercept provides offset boosting for a variable.
  • Independent control over amplitude, frequency, and offset is achieved.
  • The system is implemented using two potentiometers for practical control.

Conclusions:

  • A novel, easily controllable chaotic oscillator has been developed.
  • The system offers a convenient platform for chaos-based applications due to its tunable parameters.
  • This class of chaotic oscillators is, to the best of our knowledge, reported for the first time.