We present a model of continuous-time opinion dynamics for an arbitrary number of agents that communicate over a network and form real-valued opinions about an arbitrary number of options. The model generalizes linear and nonlinear models in the literature. Drawing from biology, physics, and social psychology, we introduce an attention parameter to modulate social influence and a saturation function to bound inter-agent and intra-agent opinion exchanges. This yields simply parameterized dynamics that exhibit the range of opinion formation behaviors predicted by model-independent bifurcation theory but not exhibited by linear models or existing nonlinear models. Behaviors include rapid and reliable formation of multistable consensus and dissensus states, even in homogeneous networks, as well as ultra-sensitivity to inputs, robustness to uncertainty, flexible transitions between consensus and dissensus, and opinion cascades. Augmenting the opinion dynamics with feedback dynamics for the attention parameter results in tunable thresholds that govern sensitivity and robustness. The model provides new means for systematic study of dynamics on natural and engineered networks, from information spread and political polarization to collective decision making and dynamic task allocation.

中文翻译：

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具有可调灵敏度的意见动力学的一般模型

我们为任意数量的代理提供了一个连续时间意见动态模型，这些代理通过网络进行通信并形成关于任意数量选项的实值意见。该模型概括了文献中的线性和非线性模型。借鉴生物学、物理学和社会心理学，我们引入了一个注意力参数来调节社会影响和一个饱和函数来限制代理间和代理内的意见交换。这产生了简单的参数化动态，它展示了由独立于模型的分叉理论预测的意见形成行为的范围，但没有由线性模型或现有的非线性模型展示。行为包括快速可靠地形成多稳定共识和分歧状态，即使在同构网络中，以及对输入的超敏感，对不确定性的稳健性、共识与分歧之间的灵活转换以及意见级联。用注意力参数的反馈动态增强意见动态会产生可调节的阈值，这些阈值控制敏感性和鲁棒性。该模型为系统研究自然和工程网络的动态提供了新方法，从信息传播和政治极化到集体决策和动态任务分配。