Asymmetrical effect of migration on a prey–predator model

We present a lattice model, where prey and predator randomly walk with different rates. Computer simulations explain the asymmetrical effect: predators more frequently migrate than preys. Moreover, we find that the aggregation of species is promoted by diffusion process.

[1]  R. Durrett Lecture notes on particle systems and percolation , 1988 .

[2]  Kei-ichi Tainaka,et al.  Indirect relation between species extinction and habitat destruction , 2001 .

[3]  N. Britton Essential Mathematical Biology , 2004 .

[4]  Kei-ichi Tainaka,et al.  Lattice Model for the Lotka-Volterra System , 1988 .

[5]  N. Inui,et al.  CRITICAL BEHAVIOR OF THE CONTACT PROCESS WITH PARITY CONSERVATION , 1998 .

[6]  Kei-ichi Tainaka,et al.  Spatial Pattern in a Chemical Reaction System: Prey and Predator in the Position-Fixed Limit , 1992 .

[7]  T. Antal,et al.  Critical behavior of a lattice prey-predator model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Norio Konno,et al.  Upper bounds for survival probability of the contact process , 1991 .

[9]  Y. Iwasa,et al.  Population persistence and spatially limited social interaction. , 1995, Theoretical population biology.

[10]  K. Tainaka,et al.  Spatial enhancement of population uncertainty near the extinction threshold , 2004 .

[11]  Front motion in an A+B-->C type reaction-diffusion process: effects of an electric field. , 2004, The Journal of chemical physics.

[12]  Timothy H. Keitt,et al.  Spatial heterogeneity and anomalous kinetics: emergent patterns in diffusion-limited predatory-prey interaction , 1995 .

[13]  T. E. Harris Contact Interactions on a Lattice , 1974 .

[14]  Tomé,et al.  Stochastic lattice gas model for a predator-prey system. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.