论文标题
沿着Lotka-Volterra竞争模型的分离速度降低了严重的速度
Critical Slowing Down along the Separatrix of Lotka-Volterra Model of Competition
论文作者
论文摘要
Lotka-Volterra竞争模型已通过使用Runge-Kutta-Fehlberg算法进行数值模拟研究。找到稳定的固定点，不稳定的固定点，马鞍节点，吸引力的盆地和分离物。系统地研究了与达到稳定固定点有关的瞬态行为。可以观察到，在吸引人的任何一个盆地中达到稳定的固定点的时间在很大程度上取决于距离分隔的初始距离。当初始点接近分隔时，这次被发现对数发散。到达稳定固定点所需的时间的差异表明在平衡相变的临界点附近的临界减速。在达到稳定的固定点之前，还观察到在马鞍固定点附近的稳定行为。
The Lotka-Volterra model of competition has been studied by numerical simulations using the Runge-Kutta-Fehlberg algorithm. The stable fixed points, unstable fixed point, saddle node, basins of attraction, and the separatices are found. The transient behaviours associated with reaching the stable fixed point are studied systematically. It is observed that the time of reaching the stable fixed point in any one of the basins of attraction, depends strongly on the initial distance from the separatrix. As the initial point approached the separatrix, this time was found to diverge logarithmically. The divergence of the time, required to reach the stable fixed point, indicates the critical slowing down near the critical point in equilibrium phase transition. A metastable behaviour was also observed near the saddle fixed point before reaching the stable fixed point.
