标题： 具有时间延迟和复制周期波动的广义准物种模型 显示英文标题

标题： Generalized Quasispecies Model with Time Delays and Periodic Fluctuations in Replication

摘要： 在这项研究中，我们提出了一种广义的准物种模型，其中种群增长由一个包含时间延迟的任意非线性函数所支配。 我们首先证明，在种群数量恒定的约束下，带有时间延迟的系统的动力学在正向和反向时间演化中仍然局限于不变流形上。 此外，我们建立了一个修改后的准物种模型，在单峰适应度景观上，当存在反向突变以及复制速率和复制概率的周期性波动时，第$i$种复制物种的浓度表现出与时间延迟大小无关的周期性行为。 具体来说，这种浓度在与错误复制相关的概率$Q_{ji}$的最小值和最大值之间振荡；也就是说，类型为$j$的突变复制子产生类型为$i$的后代的概率。 此外，在存在时间延迟和复制速率的非恒定周期性波动的情况下，我们证明如果类型为$j$的突变复制子产生类型为$i$的后代的概率在所有复制子中保持恒定，那么唯一的正周期解必然是一个常数解。 显示英文摘要

摘要： In this research, we present a generalized quasispecies model in which population growth is governed by an arbitrary nonlinear function incorporating time delays. We begin by demonstrating that, under the constant population constraint, the dynamics of the system with time delays remain confined to the invariant manifold for both forward and backward time evolution. Furthermore, we establish that in this modified quasispecies model, defined on a single-peak fitness landscape, in the presence of backward mutation and periodic fluctuations in replication rates and in replication probabilities, the concentration of the $i$th replicating species exhibits a periodic behavior in time independent of the magnitude of the time delays. Specifically, this concentration oscillates between the minimum and maximum values of the probabilities $Q_{ji}$ associated with erroneous replication; that is, the probability that a mutated replicator of type $j$ produces an offspring of type $i$. Moreover, under the presence of time delays and non-constant periodic fluctuations in replication rates, we show that if the probability that a mutated replicator of type $j$ produces an offspring of type $i$ remains constant across all replicators, then the unique positive periodic solution is necessarily a constant solution.