Biased random walks and propagation failure.

Vicenç Méndez, Sergei Fedotov, Daniel Campos, Werner Horsthemke

    Research output: Contribution to journalArticlepeer-review


    The critical value of the reaction rate able to sustain the propagation of an invasive front is obtained for general non-Markovian biased random walks with reactions. From the Hamilton-Jacobi equation corresponding to the mean field equation we find that the critical reaction rate depends only on the mean waiting time and on the statistical properties of the jump length probability distribution function and is always underestimated by the diffusion approximation. If the reaction rate is larger than the jump frequency, invasion always succeeds, even in the case of maximal bias. Numerical simulations support our analytical predictions.
    Original languageEnglish
    JournalPhysical review. E, Statistical, nonlinear, and soft matter physics
    Issue number1 Pt 1
    Publication statusPublished - Jan 2007


    Dive into the research topics of 'Biased random walks and propagation failure.'. Together they form a unique fingerprint.

    Cite this