DYNAMICAL-SYSTEMS UNDER CONSTANT ORGANIZATION .3. COOPERATIVE AND COMPETITIVE BEHAVIOR OF HYPERCYCLES
DYNAMICAL-SYSTEMS UNDER CONSTANT ORGANIZATION .3. COOPERATIVE AND COMPETITIVE BEHAVIOR OF HYPERCYCLES
复制标题
DOI：
10.1016/0022-0396(79)90039-1
复制
发表时间：
1979-01-01
影响因子：
2.4
通讯作者：
WOLFF, R
中科院分区：
文献类型：
--
作者：
SCHUSTER, P;SIGMUND, K;WOLFF, R
方程（1.1）在最近的生物大分子自组织理论中起着核心作用，该理论重点关注催化超循环的概念（[l]，[2]）。我们解释 s；作为物种 i 的（相对）浓度。这些物种形成一个循环：物种 i 的生长由其“前身”i-1 通过 Michaelis-Menten 型反应催化。@ 通过保持总浓度固定来充当“选择压力”。 int S, 中存在唯一的不动点 C，由关系式 k, xiel= kjxjel 和 (1.3) 给出。 [3]中表明，如果所有 k 都相等，则 C 是 11:= 2 和 3 的汇点，不再是汇点，但对于 n= 4 仍渐近稳定，对于 n> 5 则不稳定。
Equation(1.1) plays a central role in the recent theory of self-organization of biological macromolecules which focuses on the notion of the catalytic hypercycle([l],[2]). We interpret s; as (relative) concentration of the species i. These species form a cycle: the growth of species i is catalysed by its “predecessor” i-1 through reactions of Michaelis-Menten type.@ acts as “selection pressure” by keeping the total concentration fixed. There exists a unique fixed point C in int S,, given by the relations k, xiel= kjxjel together with (1.3). It is shown in [3] that if all k, are equal, then C is a sink for 11:= 2 and 3, no longer a sink but still asymptotically stable for n= 4 and unstabIe for n> 5.