Mathematical Model Analysis for the Stability Change of Ecosystem by Elimination of Interspecific Relationship

1.对于具有暂时间歇竞争关系的Lotka-Volterra两种群竞争系统，暂时间歇竞争既可以实现共存，也可以强调竞争。此外，我们还介绍了这两种物种的空间分布，建立了反应扩散系统的数学模型，并将空间分布的扩张或收缩作为行波问题来讨论。到目前为止，我们发现时间上的间歇性竞争可以导致两个物种在同一地点共存，它们的空间分布是重叠的。从数学上讲，在不考虑空间分布的情况下，这种共址共存的条件将与种群动态的共存条件密切相关。此外，在空间共存的情况下，每个空间分布都会侵入另一个物种的栖息地。数值计算表明，Suc…锋面更多的h空间入侵可以看作是一个恒定速度的定常行波。对于Lotka-Volterra捕食者-食饵系统，我们研究了捕食者与被捕食者共存的可能性，这种竞争中介了捕食者与被捕食者的明显竞争。我们可以证明，即使一个猎物由于一个捕食者喂养另一个猎物的捕食而趋于灭绝，如果它与另一个猎物(S)有适当的竞争关系，无论捕食者灭绝与否，猎物都可以生存。这意味着，随着食物网中猎物之间的竞争关系的消除，一些猎物可能会因为这种间接影响而灭绝。结果表明，竞争关系可以促进竞争物种之间的共存。因此，一个稳定的生态系统中的竞争关系可能会稳定系统。另一方面，新物种的入侵可能会极大地破坏系统的稳定，这取决于入侵物种可能被捕食的可能性较小。

1. As for Lotka-Volterra competing two species system with temporally intermittent competitive relationship, the temporally intermittent competition could realize the coexistence or emphasize the competition as a result. We introduce in addition the spatial distribution of those two species, making a mathematical model with reaction-diffusion system, and discuss the expansion or the shrinking of spatial distribution as a travelling wave problem. Until now we find that the temporally intermittent competition could cause the coexistence of two species at the same site, with their spatially overlapping distributions. Mathematically the conditions for such co-location coexistence would be closely related to the condition for coexistence in case of population dynamics without taking account of spatial distribution. Moreover, in case of spatial co-location coexistence, each spatial distribution invades into the habitat of another species. Numerical calculations indicate that the front of suc … More h spatial invasion can be treated as a stationary travelling wave with a constant speed2. As for Lotka-Volterra predator-prey system, we investigate the possibility of coexistence of preys with competition which mediates the apparent competition by a common predator. We can show that, even when a prey tends to go extinct due to predation by a predator that feeds another preys, the prey could survive if it has an appropriate competitive relationship with another prey(s), with or without predators extinction. This implies that, with an elimination of competitive relationship between preys within a food web, some preys could go extinct due to such indirect effect. Consequently it is indicated that the competitive relationship could promote the coexistence between those competing species. Therefore, the competitive relationship within a stable ecosystem may stabilize the system. On the other hand, the invasion of new species may considerably destabilize the system, depending on the possible predation for the invading species Less