具有随机速率的二维May-Leonard模型的共存性
Co-existence in the two-dimensional May-Leonard model with random rates
摘要：
我们采用Monte Carlo模拟数值研究的时间演化和瞬态振荡的人口密度，相关的频率功率谱，和空间相关函数的（准）稳态在二维随机May-伦纳德模型的移动个人，允许与最近的邻居和跳跃到空站点的粒子交换。因此，我们考虑一类总粒子数不守恒的四态三种群循环捕食模型。我们表明，淬火无序的反应或在流动率几乎没有影响的动态演化，螺旋图案的出现和结构，或在这个系统中的平均消光时间。我们还表明，直接的粒子对交换过程促进规则的螺旋结构的形成。此外，随着迁移率的增加，我们观察到May-Leonard系统的消光性质发生了显著的变化（对于小型系统）：（1）当迁移率超过将物种共存（准）稳态与吸收态分开的阈值时，作为系统尺寸N的函数的平均消光时间从函数形式~ e^{cN} / N交叉（其中c是常数）到线性依赖性;（2）消光时间的测量直方图显示从（近似）指数分布到高斯分布的对应交叉。后者的结果也成立时，发现流动率是随机分布的。
英文摘要：
We employ Monte Carlo simulations to numerically study the temporal evolution and transient oscillations of the population densities, the associated frequency power spectra, and the spatial correlation functions in the (quasi-)steady state in two-dimensional stochastic May--Leonard models of mobile individuals, allowing for particle exchanges with nearest-neighbors and hopping onto empty sites. We therefore consider a class of four-state three-species cyclic predator-prey models whose total particle number is not conserved. We demonstrate that quenched disorder in either the reaction or in the mobility rates hardly impacts the dynamical evolution, the emergence and structure of spiral patterns, or the mean extinction time in this system. We also show that direct particle pair exchange processes promote the formation of regular spiral structures. Moreover, upon increasing the rates of mobility, we observe a remarkable change in the extinction properties in the May--Leonard system (for small system sizes): (1) As the mobility rate exceeds a threshold that separates a species coexistence (quasi-)steady state from an absorbing state, the mean extinction time as function of system size N crosses over from a functional form ~ e^{cN} / N (where c is a constant) to a linear dependence; (2) the measured histogram of extinction times displays a corresponding crossover from an (approximately) exponential to a Gaussian distribution. The latter results are found to hold true also when the mobility rates are randomly distributed.
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