The Multitype Contact Process with Frozen States or Allelopathy Model
نویسنده
چکیده
The aim of this paper is to study a generalization of the two colors multitype contact process intended to mimic an example of interspecific competition called allelopathy. Roughly speaking, the strategy of the first species is to inhibit the growth of the second one by freezing the sites it has colonized. Our main objective is to prove that this spatial model exhibits some phase transitions comparable with those of the classical multitype contact process. In particular, we show that depending on its birth rate each species may conquer the other one.
منابع مشابه
A Multitype Contact Process with Frozen Sites: a Spatial Model of Allelopathy
In this paper, we introduce a generalization of the two-color multitype contact process intended to mimic a biological process called allelopathy. To be precise, we have two types of particle. Particles of each type give birth to particles of the same type, and die at rate 1. When a particle of type 1 dies, it gives way to a frozen site that blocks particles of type 2 for an exponentially distr...
متن کاملTwo-Scale Multitype Contact Process: Coexistence in Spatially Explicit Metapopulations∗
It is known from past research that the limiting behavior of the contact process strongly depends upon the geometry of the graph on which particles evolve: while the contact process on regular lattices exhibits only two phases, the process on homogeneous trees exhibits an intermediate phase of weak survival. Similarly, we prove that the geometry of the interaction network can drastically affect...
متن کاملSome rigorous results for the stacked contact process
The stacked contact process is a stochastic model for the spread of an infection within a population of hosts located on the d-dimensional integer lattice. Regardless of whether they are healthy or infected, hosts give birth and die at the same rate and in accordance to the evolution rules of the neutral multitype contact process. The infection is transmitted both vertically from infected paren...
متن کاملCentral Limit Theorem in Multitype Branching Random Walk
A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.
متن کاملThe shelf-life of conventional surimi and recovery of functional proteins from silver carp (Hypophthalmichthys molitrix) muscle by an acid or alkaline solubilization process during frozen storage
The shelf-life of conventional surimi and isolated proteins that modified by acidic pH (2.5) and by using alkali pH (11) from silver carp (Hypophthalmichthys molitrix) was studied during months of storage at -18±2 °C. For conventional surimi, three washing steps were used. In the third stage of washing, 0.2% NaCl was used to withdraw more water. The result showed that isolated protein by alkali...
متن کامل