Significance Political polarization threatens democracy in America. This article helps illuminate what drives it, as well factors account for its asymmetric nature. In particular, we focus on positive feedback among members of Congress the key mechanism polarization. We show how public opinion, which responds to laws legislators make, turn dynamics political elites. Specifically, find that voters’ “policy mood,” i.e., whether opinion leans a more liberal or conservative direction,...

We propose a continuous-time multi-option nonlinear generalization of classical linear weighted-average opinion dynamics.Nonlinearity is introduced by saturating exchanges, and this enough to enable significantly greater range opinion-forming behaviors with our model as compared existing models.For group agents that communicate opinions over network, these include multistable agreement disagreement, tunable sensitivity input, robustness disturbance, flexible transition between patterns...

Cognitive stability and flexibility are regarded as key ingredients of goal-directed behavior. This review introduces dynamical systems a theoretical framework for studying cognitive stability. Following gentle introduction to theory, we discuss how can be operationalized examined through the lens such models. Drawing from recent advances in argue that various models stability, ranging spiking neurons human task switching collective animal behavior, understood terms same mathematical...

.How does a group of agents break indecision when deciding about options with qualities that are hard to distinguish? Biological and artificial multiagent systems, from honeybees bird flocks bacteria, robots, humans, often need overcome choosing among in situations which the performance or even survival is at stake. Breaking also important because fully indecisive state, where not biased toward any specific option, agent maximally sensitive prone adapt inputs changes its environment. Here,...

A multiagent system should be capable of fast and flexible decision-making to successfully manage the uncertainty, variability, dynamic change encountered when operating in real world. Decision-making is if it breaks indecision as quickly becomes costly. This requires divergence away from addition convergence a decision. adapts signals important successful operation, even they are weak or rare. tunable sensitivity input for modulating regimes which ultrasensitive robust. Nonlinearity...

We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model opinion dynamics. Each modeled agent updates its real-valued about each available strategy response to payoffs and other agents' opinions, as observed over a network. show how provides principled systematic means investigate agents that select strategies rationality reciprocity, key features human decision-making social dilemmas. For two-strategy...

We propose a new decentralized design to control opinion patterns on signed networks of agents making decisions about two options and switch the network from any pattern desired one. Our method relies switching transformations, which sign an agent's at stable equilibrium by flipping interactions with its neighbors. The global dynamical behavior switched can be predicted rigorously when original, thus switched, are structurally balanced. Structural balance ensures that dynamics monotone,...

When communicating agents form opinions about a set of possible options, agreement and disagreement are both outcomes. Depending on the context, either can be desirable or undesirable. We show that for nonlinear opinion dynamics networks, variety network structures, spectral properties underlying adjacency matrix fully characterize occurrence disagreement. further how corresponding eigenvector centrality, as well any symmetry in network, informs resulting patterns formation agent sensitivity...

We introduce and analyze a continuous time state-space model of opinion cascades on networks large numbers agents that form opinions about two or more options. By leveraging our recent results the emergence agreement disagreement states, we novel tools to control cascades. New notions centrality, which depend only network structure, are shown be key characterizing nonlinear behavior formation Our relevant for analysis in real-world networks, including biological, social artificial design...

We develop a model-independent framework to study the dynamics of decision-making in opinion networks for an arbitrary number agents and options. Model-independence means that analysis is not performed on specific set equations, contrast classical approaches decision making fix model analyze it. Rather, general features dynamical can be derived starting from empirically testable hypotheses about deciding agents, available options, interactions among them. After translating these empirical...

We propose a continuous-time multi-option nonlinear generalization of classical linear weighted-average opinion dynamics. Nonlinearity is introduced by saturating exchanges, and this enough to enable significantly greater range opinion-forming behaviors with our model as compared existing models. For group agents that communicate opinions over network, these include multistable agreement disagreement, tunable sensitivity input, robustness disturbance, flexible transition between patterns...

For a group of autonomous communicating agents to carry out coordinated objectives, it is paramount that they can distinguish meaningful input from disturbance, and come rapidly reliably agreement or disagreement in response input. We study how opinion formation cascades through networked decision makers distributed signal. Using nonlinear dynamics model with dynamic feedback modulation an attention parameter, we prove the triggering cascade collective itself depend on both node centrality...

<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q. How would you pitch your Ph.D. dissertation in one paragraph?</b>

We study the dynamics of belief formation on multiple interconnected topics in networks agents with a shared system. establish sufficient conditions and necessary under which sustained oscillations beliefs arise network Hopf bifurcation characterize role communication graph system shaping relative phase amplitude patterns oscillations. Additionally, we distinguish broad classes graphs that exhibit such from those do not.

We propose and analyze a nonlinear dynamic model of continuous-time multi-dimensional belief formation over signed social networks. Our accounts for the effects structured system, self-appraisal, internal biases, various sources cognitive dissonance posited by recent theories in psychology. prove that strong beliefs emerge on network as consequence bifurcation. how balance controls nature bifurcation and, therefore, belief-forming limit-set solutions. analysis provides constructive...

We present and analyze a mathematical model to study the feedback between behavior epidemic spread in population that is actively assessing reacting risk of infection. In our model, dynamically forms an opinion reflects its willingness engage risky (e.g., not wearing mask crowded area) or reduce it social distancing). consider SIS dynamics which contact rate within adapts as function opinion. For new coupled we prove existence two distinct parameter regimes. One regime corresponds low...