Related Experiment Video
Updated: May 22, 2026

Visualizing Hyporheic Flow Through Bedforms Using Dye Experiments and Simulation
Published on: November 18, 2015
Predator-prey dynamics in a uniform medium lead to directed percolation and wave-train propagation
Alexandra Agranovich1, Yoram Louzoun
1Department of Mathematics and Gonda Brain Research Center, Bar-Ilan University, Ramat Gan 52900, Israel.
Abstract:
The dynamics of birth-death processes with extinction points that are unstable in the deterministic average description has been extensively studied, mainly in the context of the stochastic transition from the mean-field attracting fixed point to the absorbing state. Here we study the opposite case of a small perturbation from the zero-population absorbing state. We show that such perturbations can grow beyond the mean-field attracting fixed point and then can collapse back into the absorbing state. Such dynamics can represent, for example, the fast growth of a pathogen and then its destruction by the immune system. We show that when the prey perturbation extinction probability is high, the loss of synchronization between the prey densities in different regions in space leads to two possible dynamic regimes: (a) a directed percolation regime based on the balance between regions escaping the absorbing state and regions absorbed into it, and (b) wave trains representing the transition of the entire space to the mean-field stable positive fixed point.
Related Concept Videos
Propagation of Waves
Consider a scenario where a wave propagates from a string of low linear mass density to a string of high linear mass density. In such a case, the reflected wave is out of phase with respect to the incident wave, however the...
Travelling Waves
Water waves, sound waves, and seismic waves are some examples of mechanical waves. For water waves, the wave propagation medium is water;...
Velocity and Acceleration of a Wave
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...
Propagation Speed of Electromagnetic Waves
Traveling Waves: Lossless Lines
Uniform Depth Channel Flow

