The motivation for the proposed work is drawn from the attachment-detachment observed in biological and physical transport processes that entail finite resources. We investigate the influence of limited particle availability on particle dynamics within two parallel totally asymmetric simple exclusion lanes, with one lane incorporating only particle detachment and the other considering particle attachment. We establish a theoretical framework by employing vertical mean-field theory in conjunction with singular perturbation technique. The analytical findings are supported by numerical and stochastic validation using a finite-difference scheme and the Gillespie algorithm. By utilizing these approaches, we scrutinize various stationary properties, including particle densities, phase boundaries, and particle currents for both lanes. Our analysis reveals that the complexity of the phase diagram exhibits a nonmonotonic trend in the number of stationary phases as the particle count increases. Each phase diagram is constructed with respect to the intrinsic boundary parameters, illustrating both bulk and surface transitions occurring within the lanes. The interplay between finite resources and coupling mechanisms gives rise to two phases involving upward shock in one of the lanes, while two phases exhibit synchronized downward shock in both lanes. Finally, we delve into shock dynamics to comprehend critical phase transitions occurring in the system.

中文翻译：

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具有偏向换道机制的排除模型中的资源竞争

拟议工作的动机来自于在需要有限资源的生物和物理运输过程中观察到的依恋分离。我们研究了两个平行的完全不对称简单排除通道内有限的粒子可用性对粒子动力学的影响，其中一个通道仅包含粒子分离，另一个通道考虑粒子附着。我们通过采用垂直平均场理论结合奇异摄动技术建立了一个理论框架。分析结果得到了使用有限差分方案和 Gillespie 算法的数值和随机验证的支持。通过利用这些方法，我们仔细检查了各种稳态特性，包括两个泳道的粒子密度、相界和粒子电流。我们的分析表明，随着颗粒计数的增加，相图的复杂性在固定相数量上呈现出非单调趋势。每个相图都是根据固有边界参数构建的，说明了泳道内发生的体积和表面转变。有限资源和耦合机制之间的相互作用产生了两个阶段，其中一个通道中涉及向上冲击，而两个阶段在两个通道中都表现出同步的向下冲击。最后，我们深入研究冲击动力学，以理解系统中发生的关键相变。