论文标题
自组织层次结构形成的分段线性模型
A piecewise linear model of self-organized hierarchy formation
论文作者
论文摘要
通过对Sigmoid函数的分段线性近似，研究了自组织层次结构形成的Bonabeau模型。分段线性代理模型的仿真表明，存在两级和三级分层解，并且每个代理都表现出从非共性行为到厄尔贡行为的过渡。此外，通过对试剂模型使用平均场近似值，分析表明，即使模型方程是对称的（仅在初始条件下引入不对称），并且是线性稳定且不稳定的三级解决方案，即使模型方程是对称的，也存在不对称的两级溶液。还表明，其中一些解决方案通过不变子空间中的超临界叉状分叉出现。还介绍了平均场模型中线性层次结构解决方案的存在和稳定性。
The Bonabeau model of self-organized hierarchy formation is studied by using a piecewise linear approximation to the sigmoid function. Simulations of the piecewise-linear agent model show that there exist two-level and three-level hierarchical solutions, and that each agent exhibits a transition from non-ergodic to ergodic behaviors. Furthermore, by using a mean-field approximation to the agent model, it is analytically shown that there are asymmetric two-level solutions, even though the model equation is symmetric (asymmetry is introduced only through the initial conditions), and that linearly stable and unstable three-level solutions coexist. It is also shown that some of these solutions emerge through supercritical-pitchfork-like bifurcations in invariant subspaces. Existence and stability of the linear hierarchy solution in the mean-field model are also presented.
