Kinetic Behaviors of a Competitive Population and Fitness System
in Exchange-Driven Growth |
| |
Authors: | LU Ke LIN Zhen-Quan SUN Yun-Fei |
| |
Institution: | Department of Physics, Wenzhou University, Wenzhou 325027, China |
| |
Abstract: | We proposed an aggregation model of two species aggregates of fitness and population to study the interaction between the two species in their exchange-driven processes of the same species by introducing the monomer birth of fitness catalyzed by the
population, where the fitness aggregates perform self-death
process and the population aggregates perform self-birth process. The kinetic behaviors of the aggregate size distributions of the fitness and population were analyzed by the rate equation approach with their exchange rate kernel K1(k,j)=K1kj and
K2(k,j)=K2kj, the fitness aggregate's self-death rate
kernel J1(k)=J1k, population aggregate's self-birth rate
kernel J2(k)=J2k and population-catalyzed fitness birth rate kernel
I(k,j)=Ikju. The kinetic behavior of the fitness was found depending crucially on the parameter u,
which reflects the dependence of the population-catalyzed fitness birth rate on the size of the catalyst (population) aggregate. (i)
In the u ≤0 case, the effect of catalyzed-birth of fitness is rather weak and the exchange-driven aggregation and self-death of the fitness dominate the process, and the fitness aggregate size distribution ak(t) does not have scale form. (ii) When u>0, the effect of the population-catalyzed birth of
fitness gets strong enough, and the catalyzed-birth and self-death
of the fitness aggregates, together with the self-birth of the
population aggregates dominate the evolution process of the
fitness aggregates. The aggregate size distribution ak(t)
approaches a generalized scaling form. |
| |
Keywords: | kinetic behavior aggregate growths catalyzed-birth rate equations |
|
| 点击此处可从《理论物理通讯》浏览原始摘要信息 |
| 点击此处可从《理论物理通讯》下载免费的PDF全文 |
|