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Related Experiment Videos

Transforming complex multistability to controlled monostability.

Binoy Krishna Goswami1, Sourish Basu

  • 1Laser and Plasma Technology Division, Bhabha Atomic Research Centre, Mumbai 400085, India. bgoswami@apsara.barc.ernet.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

Controlling complex nonlinear systems is now possible. Slow, weak periodic parameter modulation transforms multistable systems into monostable ones, even in noisy conditions, by eliminating unwanted stable states.

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Multistability, characterized by multiple coexisting stable states, is common in nonlinear systems.
  • High multistability can arise in low-dissipative systems, posing control challenges.
  • The Hénon map serves as a standard model for studying nonlinear dynamics and multistability.

Purpose of the Study:

  • To demonstrate a method for controlling multistable nonlinear systems.
  • To transform complex multistable systems into controlled monostable systems.
  • To investigate the effectiveness of periodic parameter modulation for control.

Main Methods:

  • Applying slow and weak periodic parameter modulation to the Hénon map.
  • Analyzing the system's behavior in low-dissipative regimes.

Related Experiment Videos

  • Observing the impact of modulation on coexisting stable states, including in the presence of noise.

    • Main Results:

    • Periodic parameter modulation effectively transforms multistable systems into monostable ones.
    • The method successfully eliminates coexisting stable states, even in the low-dissipative limit.
    • Controlled monostability is achieved by driving the system to the period-1 branch, robustly in the presence of noise.

    Conclusions:

    • Slow and weak periodic parameter modulation is a viable control strategy for complex nonlinear systems.
    • This technique offers a robust way to achieve controlled monostability, overcoming challenges posed by high multistability and noise.
    • The Hénon map serves as a validated model for demonstrating this control method.