Gene

Quantum mechanics

Control (management)

Engineering

Discrete mathematics

Dynamics (music)

Robustness (evolution)

Biochemistry

Computer science

Acoustics

Physics

Nonlinear system

Mathematics

Electronic engineering

Mathematical analysis

Artificial intelligence

Sensitivity (control systems)

Network dynamics

Chemistry

Control theory (sociology)

Generalization

IEEE Transactions on Automatic Control

We propose a continuous-time multi-option nonlinear generalization of classical linear weighted-average opinion dynamics.Nonlinearity is introduced by saturating opinion exchanges, and this is enough to enable a significantly greater range of opinion-forming behaviors with our model as compared to existing linear and nonlinear models.For a group of agents that communicate opinions over a network, these behaviors include multistable agreement and disagreement, tunable sensitivity to input, robustness to disturbance, flexible transition between patterns of opinions, and opinion cascades.We derive networkdependent tuning rules to robustly control the system behavior and we design state-feedback dynamics for the model parameters to make the behavior adaptive to changing external conditions.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. I. INTRODUCTION.Opinion dynamics of networked agents are the subject of long-standing interdisciplinary interest, and there is a large and growing literature on agent-based models created to study mechanisms that drive the formation of consensus and opinion clustering in groups.These models appear, for example, in studies of collective animal behavior and voting patterns in human social networks.In engineering, they are fundamental to designing distributed coordination of autonomous agents and dynamic allocation of tasks across a network.Agent-based models are typically used to investigate parameter regimes and network structures for which opinions in a group converge over time to a desired configuration.However, natural groups exhibit much more flexibility than captured with existing models.Remarkably, groups in nature can rapidly switch between different opinion configurations in response to changes in their environment, and they can break deadlock, i.e., choose among options with little, if any, evidence that one option is better than another.Understanding the mechanisms that explain the temporal dynamics of opinion formation in groups and the ultra-sensitivity and robustness needed for groups to pick out meaningful information and to break deadlock in uncertain and changing environments is

Nonlinear Opinion Dynamics With Tunable Sensitivity