Population extinction in a time-modulated environment

Michael Assaf*, Alex Kamenev, Baruch Meerson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


The extinction time of an isolated population can be exponentially reduced by a periodic modulation of its environment. We investigate this effect using, as an example, a stochastic branching-annihilation process with a time-dependent branching rate. The population extinction is treated in eikonal approximation, where it is described as an instanton trajectory of a proper reaction Hamiltonian. The modulation of the environment perturbs this trajectory and synchronizes it with the modulation phase. We calculate the corresponding change in the action along the instanton using perturbation techniques supported by numerical calculations. The techniques include a first-order theory with respect to the modulation amplitude, a second-order theory in the spirit of the Kapitsa pendulum effect, and adiabatic theory valid for low modulation frequencies.

Original languageAmerican English
Article number041123
JournalPhysical Review E
Issue number4
StatePublished - 27 Oct 2008


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