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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Published on: June 8, 2018

Simple driven chaotic oscillators with complex variables.

Delmar Marshall1, J C Sprott

  • 1Department of Physics, Amrita Vishwa Vidyapeetham, Kollam, Kerala, India.

Chaos (Woodbury, N.Y.)
|April 2, 2009
PubMed
Summary
This summary is machine-generated.

Researchers found no chaotic solutions for driven complex-variable oscillators with polynomial f(z). However, seven new chaotic oscillators of the form z+f(z,z)=e(iOmegat) were discovered, exhibiting complex dynamics and various routes to chaos.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems
  • Chaos Theory

Background:

  • Driven complex-variable oscillators are theoretical models for various physical phenomena.
  • Previous research has explored the conditions for chaotic behavior in such systems.
  • The specific forms z+f(z)=e(iOmegat) and z+f(z,z)=e(iOmegat) were investigated.

Purpose of the Study:

  • To determine if driven complex-variable oscillators of the form z+f(z)=e(iOmegat) can exhibit chaotic solutions.
  • To identify and characterize new examples of driven chaotic oscillators.
  • To analyze the parameter-dependent behavior of these chaotic systems.

Main Methods:

  • Analytical investigation of differential equations for complex-variable oscillators.
  • Numerical simulations to generate and visualize chaotic attractors.
  • Calculation of Lyapunov spectra to quantify chaotic behavior.
  • Systematic variation of the control parameter Omega.

Main Results:

  • Proven that driven complex-variable oscillators with analytic f(z) cannot have chaotic solutions.
  • Presented seven novel driven chaotic oscillators of the form z+f(z,z)=e(iOmegat).
  • Observed diverse routes to chaos including period doubling, intermittency, chaotic transients, and period adding.
  • Identified attractors with x=-y symmetry and numerous instances of coexisting attractors.

Conclusions:

  • The form of the nonlinear function f is critical in determining the possibility of chaos in driven complex-variable oscillators.
  • New models provide platforms for studying complex nonlinear phenomena.
  • The rich dynamics observed highlight the sensitivity of these systems to parameter changes.