BECS: Pattern-Steering in Nonlinear Dynamical Networks

我们研究了将复杂动态网络的活动从一种状态移动到另一种状态的计算方法。复杂的非线性网络表现为多稳定和多节奏，是混沌和周期稳定吸引子的混合，以及在工程应用的时间间隔内可能有效稳定的其他亚稳态瞬态。计算方法将用于在吸引子盆地之间进行转向，并在三个不同的实验平台上进行测试：来自脊椎动物和无脊椎动物的初级神经元细胞培养，来自啮齿动物的海马切片，以及向列液晶中对流卷的缺陷活动。更好地理解这些测试用例可能是神经工程、机器学习以及能量传递和生产优化新方法的第一步。实验实例都缺乏已知的运动方程，这严重限制了经典控制理论的使用，并激发了我们新技术的发展。工程设备中复杂系统行为的标志是在时间和空间中变化的动态模式的出现。在这项探索性研究中，我们将揭示在工程网络中实现不同时空模式之间的低功率转向需要克服的主要问题和瓶颈，并开始开发有效的计算方法来快速自动地完成这种切换。该项目包括理论、计算和实验部分。方法将在具有非线性、复杂网络特征的系统中开发和实验测试，如原代神经元细胞培养、啮齿动物海马切片和向列液晶。

We investigate computational methods for moving the activity of a complex dynamical network from one state to another. Complicated nonlinear networks appear to be multistable and multirhythmic, a mix of chaotic and periodic stable attractors, together with other metastable transients that may be effectively stable for the time interval of an engineering application. Computational methods will be developed for steering between basins of attractors, and tested in three different experimental platforms: primary neuronal cell cultures from vertebrates and invertebrates, hippocampal slices from rodents, and defect activity in convection rolls in nematic liquid crystals. Better understanding of these test cases could be a first step to new approaches to neural engineering, machine learning, and optimization of energy transfer and production. The experimental examples have in common a lack of known equations of motion, which severely limits the use of classical control theory and motivates development of our new techniques.The hallmark of complex systems behavior in engineering devices is the appearance of dynamical patterns that vary in time and space. In this exploratory study, we will expose the main problems and bottlenecks that need to be overcome to enable low-power steering between different spatiotemporal patterns in engineered networks, and to begin to develop efficient computational methods to accomplish this switching quickly and automatically. The project includes theoretical, computational, and experimental components. Methods will be developed and tested experimentally in systems that have nonlinear, complex network characteristics, such as primary neuronal cell cultures, hippocampal slices from rodents, and nematic liquid crystals.