Analysis of a Continuous Opinion and Discrete Action Model Coupled with an External Dynamics

We consider a set of consumers in a city or town whose opinion is governed by a continuous opinion and discrete action (CODA) dynamics model. This dynamics is coupled with an observation signal dynamics, which defines the information on the common pollution that the consumers can access. We show that the external observation signal has a significant impact on the asymptotic behavior of the CODA model. When the coupling is strong, it induces either a chaotic behavior or convergence towards a limit cycle. When the coupling is weak, a more classical behavior characterized by local agreements in polarized clusters is observed. In both cases, conditions under which clusters of consumers don't change their actions are provided. Numerical examples are provided to illustrate the derived analytical results.