论文标题
布尔网络中带有发射记忆的吸引子景观
Attractor landscapes in Boolean networks with firing memory
论文作者
论文摘要
在本文中，我们研究了带有发射记忆的布尔网络的动态行为，即布尔网络，其顶点是同步更新的，具体取决于其适当的布尔局部过渡功能，以使每个顶点保持射击状态有限的步骤。我们特别证明，这些网络与经典网络具有相同的计算能力，即任何带有$ m $顶点的启动内存的布尔网络都可以通过添加顶点来模拟。我们还证明了特定类别类别类别的一般结果。例如，我们表明，在析取网络中至少存在大于1的延迟，使此类网络仅作为吸引子的固定点。此外，对于由两个顶点组成的任意网络，我们表征了延迟相空间，即延迟值，使网络允许限制周期或固定点。最后，我们通过引入延迟来分析两个经典的生物学模型：$λ$ - 噬菌体的免疫控制模型以及植物\ emph {拟南芥thaliana}的花卉形态发生的遗传控制的模型。
In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains at its firing state a finite number of steps. We prove in particular that these networks have the same computational power than the classical ones, ie any Boolean network with firing memory composed of $m$ vertices can be simulated by a Boolean network by adding vertices. We also prove general results on specific classes of networks. For instance, we show that the existence of at least one delay greater than 1 in disjunctive networks makes such networks have only fixed points as attractors. Moreover, for arbitrary networks composed of two vertices, we characterize the delay phase space, \ie the delay values such that networks admits limit cycles or fixed points. Finally, we analyze two classical biological models by introducing delays: the model of the immune control of the $λ$-phage and that of the genetic control of the floral morphogenesis of the plant \emph{Arabidopsis thaliana}.
