标题： 从秩序到混合体：通过非线性生长解析活性流体中的动态模式 显示英文标题

标题： From Order to Chimeras: Unraveling Dynamic Patterns in Active Fluids with Nonlinear Growth

摘要： 我们研究涉及两种调节主动应力的化学物种的活性流体系统中的模式形成：一种是快速扩散的物种（$A$），另一种是缓慢扩散的物种（$I$）。物种$A$的增长通过一个非线性逻辑项进行建模。通过线性稳定性分析，我们推导出相图，以说明参数空间中的各种动力学区域。我们的研究结果表明，佩克莱特数的增加会导致均匀稳态的不稳定化。相反，出人意料的是，$A$的非线性增长参数的增加实际上稳定了均匀稳态区域。此外，我们观察到，物种之间的更大不对称性会导致三种不同的动力学相，而低不对称性无法产生振荡不稳定性。在不稳定性区域进行的数值模拟显示了从高佩克莱特数下的不规则、无节奏配置到瞬时和稳健的对称性破缺奇异性状态的各种模式。值得注意的是，这些奇异性模式在振荡不稳定性区域更为普遍，我们的稳定性分析表明，该区域在高非线性增长参数和中等高佩克莱特数时是最广泛的。此外，我们还发现类似孤子的结构，其中物种$A$的聚集合并，并且新的聚集自发出现，这些模式在静态不稳定性阶段很普遍。总体而言，我们的研究说明，在受化学物种非线性增长影响的活性物质中，可以出现多种多样的模式，当非线性增长参数升高时，奇异性尤为显著。 显示英文摘要

摘要： We explore pattern formation in an active fluid system involving two chemical species that regulate active stress: a fast-diffusing species ($A$) and a slow-diffusing species ($I$). The growth of species $A$ is modelled using a nonlinear logistic term. Through linear stability analysis, we derive phase diagrams illustrating the various dynamical regimes in parameter space. Our findings indicate that an increase in the P\'eclet number results in the destabilisation of the uniform steady state. In contrast, counter-intuitively, an increase in the nonlinear growth parameter of $A$ actually stabilises the homogeneous steady-state regime. Additionally, we observe that greater asymmetry between the species leads to three distinct dynamical phases, while low asymmetry fails to produce oscillatory instability. Numerical simulations conducted in instability regimes show patterns that range from irregular, arrhythmic configurations at high P\'eclet numbers to both transient and robust symmetry-breaking chimera states. Notably, these chimera patterns are more prevalent in the oscillatory instability regime, and our stability analysis indicates that this regime is the most extensive for high nonlinear growth parameters and moderately high P\'eclet numbers. Further, we also find soliton-like structures where aggregations of species $A$ merge, and new aggregations spontaneously emerge, and these patterns are prevalent in the phase of stationary instability. Overall, our study illustrates that a diverse array of patterns can emerge in active matter influenced by nonlinear growth in a chemical species, with chimeras being particularly dominant when the nonlinear growth parameter is elevated.