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Reset induced multimodality in unbounded potential.

Karol Capała1

  • 1Faculty of Computer Science, AGH University of Krakow, Mickiewicza 30, 30-059 Kraków, Poland.

Chaos (Woodbury, N.Y.)
|July 1, 2025
PubMed
Summary
This summary is machine-generated.

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Resetting can create surprising stationary states in systems with repulsive forces. This study shows how resetting can lead to multiple peaks in these states, even without traditional energy wells.

Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Stochastic dynamics are fundamental to many physical and biological systems.
  • Unbounded potentials typically do not exhibit stationary states.
  • Resetting protocols can alter system dynamics, sometimes inducing stable states.

Purpose of the Study:

  • To investigate the emergence of multimodality in stationary states within unbounded potentials using resetting.
  • To explore how resetting influences the number and distribution of modes in these states.
  • To analyze the impact of noise intensity and resetting frequency on modal structure.

Main Methods:

  • Theoretical analysis of stochastic processes with resetting.
  • Numerical simulations of systems in unbounded potentials subjected to resetting.

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  • Examination of probability distributions to identify modal behavior.

    • Main Results:

    • Resetting can induce stationary states in unbounded potentials where none would normally exist.
    • These induced stationary states can exhibit multimodality (e.g., trimodal, pentamodal) despite repulsive potentials.
    • The number and shape of modes are dependent on noise intensity and resetting frequency.

    Conclusions:

    • Resetting is a powerful tool for controlling and shaping the behavior of stochastic systems.
    • Multimodal stationary states can arise in systems with repulsive potentials solely due to resetting.
    • The findings offer new insights into controlling complex system dynamics through external interventions.