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This study models predator-prey random walkers with resetting. Resetting introduces two annihilation components: a central part dependent on reset type (Cauchy for Poisson, Gaussian for sharp) and an exponentially decaying tail.

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Area of Science:

  • Statistical Physics
  • Stochastic Processes
  • Mathematical Biology

Background:

  • Random walkers are fundamental models for diffusion.
  • Resetting mechanisms introduce non-Markovian behavior and alter diffusion dynamics.
  • Understanding annihilation events in interacting random walker systems is crucial.

Purpose of the Study:

  • To analyze the annihilation dynamics of two interacting random walkers with intermittent resetting.
  • To differentiate the effects of Poissonian and sharp resetting protocols on walker annihilation.
  • To characterize the probability distribution of annihilation locations.

Main Methods:

  • Modeling the system as a pair of vicious random walkers.
  • Analytical derivation of the annihilation location distribution.
  • Numerical simulations to validate analytical findings.
  • Investigating two resetting protocols: Poissonian and sharp resetting.

Main Results:

  • In the absence of resetting, walker intersection follows a Cauchy distribution.
  • With resetting, annihilation distribution has a central part and a tail.
  • The tail of the distribution decays exponentially for both resetting types.
  • The central part exhibits a Cauchy distribution for Poisson resetting and Gaussian for sharp resetting.

Conclusions:

  • Resetting significantly alters random walker annihilation distributions.
  • The type of resetting protocol dictates the central part of the annihilation distribution.
  • Analytical predictions show good agreement with numerical simulations, validating the model.