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Chaotic synchronization: a nonlinear predictive filtering approach.

Ajeesh P Kurian1, Sadasivan Puthusserypady

  • 1Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore.

Chaos (Woodbury, N.Y.)
|April 8, 2006
PubMed
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A new nonlinear predictive filter (NPF) effectively synchronizes chaotic systems, outperforming the extended Kalman filter (EKF) in noisy conditions. The NPF avoids approximations, leading to better accuracy and faster synchronization for complex systems.

Area of Science:

  • Nonlinear dynamics
  • Control theory
  • Signal processing

Background:

  • Chaotic system synchronization is challenging due to sensitive dependence on initial conditions.
  • Noise significantly hinders perfect synchronization.
  • The extended Kalman filter (EKF) is a common but error-prone method for noisy chaotic systems, especially with high nonlinearity.

Purpose of the Study:

  • To propose a novel nonlinear predictive filter (NPF) for synchronizing chaotic systems.
  • To evaluate the performance of the NPF against the EKF.
  • To demonstrate the NPF's superiority in handling nonlinearities without Jacobian computation.

Main Methods:

  • Development of a nonlinear predictive filter (NPF).
  • Comparative numerical simulations using the NPF and EKF.

Related Experiment Videos

  • Testing on well-known chaotic systems: Lorenz and Mackey-Glass, and the Ikeda map.

    • Main Results:

    • The NPF demonstrates superior performance compared to the EKF.
    • NPF achieves lower normalized mean square error (NMSE) and total NMSE.
    • Synchronization time, measured by normalized instantaneous square error, is reduced with the NPF.

    Conclusions:

    • The NPF is a more effective algorithm for synchronizing chaotic systems in the presence of noise.
    • The NPF eliminates the need for Jacobian approximation, improving accuracy for highly nonlinear systems.
    • The proposed NPF offers a significant advancement over the EKF for chaotic system synchronization tasks.