Previous studies assumed that the reaction processes in the chemical Brusselator model are memoryless or Markovian. However, as long as a reactant interacts with its environment, the reaction kinetics cannot be described as a memoryless process. This raises a question: how do we predict the behavior of the chemical Brusselator system with molecular memory characterized by nonexponential waiting-time distributions? Here, a novel technique is developed to address this question. This technique converts a non-Markovian question to a Markovian one by introducing effective transition rates that explicitly decode the memory effect. Based on this conversion, it is analytically shown that molecular memory can induce bifurcations and oscillations. Moreover, a set of sufficient conditions are derived, which can guarantee that the system of the rate equations for the Markovian reaction system generates oscillations via memory index-induced bifurcation. In turn, these conditions can guarantee that the original non-Markovian reaction system generates stochastic oscillations. Numerical simulation verifies the theoretical prediction. The overall analysis indicates that molecular memory is not a negligible factor affecting a chemical system’s behavior.

中文翻译：

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化学布鲁塞尔模型中的记忆诱导分岔和振荡

以前的研究假设化学布鲁塞尔模型中的反应过程是无记忆的或马尔可夫的。然而，只要反应物与其环境相互作用，反应动力学就不能被描述为无记忆的过程。这就提出了一个问题：我们如何预测具有以非指数等待时间分布为特征的分子记忆的化学 Brusselator 系统的行为？在这里，开发了一种新技术来解决这个问题。该技术通过引入显式解码记忆效应的有效转换率，将非马尔可夫问题转换为马尔可夫问题。基于这种转换，分析表明分子记忆可以诱导分叉和振荡。此外，还导出了一组充分条件，这可以保证马尔可夫反应系统的速率方程组通过记忆指数诱导的分岔产生振荡。反过来，这些条件可以保证原始的非马尔可夫反应系统产生随机振荡。数值模拟验证了理论预测。整体分析表明，分子记忆并不是影响化学系统行为的一个可忽略的因素。