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Control of projective synchronization in chaotic systems.

D Xu1

  • 1Department of Engineering Mechanics, School of MPE, Nanyang Technological University, Singapore 639798, Republic of Singapore.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 20, 2001
PubMed
Summary

The scaling factor for projective synchronization in coupled systems is unpredictable, complicating state estimation. A new control method allows manipulation of this factor for preferred synchronization management.

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Area of Science:

  • Nonlinear Dynamics
  • Control Theory
  • Chaos Theory

Background:

  • Coupled dynamical systems often exhibit synchronized behavior.
  • Projective synchronization allows states to synchronize up to a scaling factor.
  • Unpredictable scaling factors hinder state estimation in partially linear systems.

Purpose of the Study:

  • To address the challenge of unpredictable scaling factors in projective synchronization.
  • To propose a novel control method for managing the synchronization scaling factor.
  • To enable preferred management of synchronized dynamics in coupled systems.

Main Methods:

  • Derivation of a control law based on the mechanism of projective synchronization.
  • Analysis of three-dimensional dynamical systems.
  • Application and illustration using the Lorenz system.

Main Results:

  • Demonstration that the scaling factor of projective synchronization is inherently unpredictable.
  • Development of a control strategy to manipulate the scaling factor to desired values.
  • Successful application of the control method to the Lorenz system.

Conclusions:

  • The unpredictability of the scaling factor poses significant challenges for state estimation.
  • The proposed control method offers a viable solution for managing projective synchronization.
  • This work provides a pathway for enhanced control and application of synchronized chaotic systems.