Emergence of chaos in interacting communities
1 Departamento de Fisica, Universidade Federal de Santa Catarina - Florianopolis, 88040-900, SC, Brazil
2 Dipartimento di Fisica, Università di Roma La Sapienza - Piazzale Aldo Moro 2, Roma I-00185, Italy
Received: 2 September 2014
Accepted: 7 October 2014
We introduce a simple dynamical model of two interacting communities whose elements are subject to stochastic discrete-time updates governed by only bilinear interactions. When the intra- and inter-couplings are cooperative, the two communities reach asymptotically an equilibrium state. However, when the intra- or inter-couplings are anti-cooperative, the system may remain in perpetual oscillations and, when the coupling values belong to certain intervals, two possible scenarios arise, characterized either by erratic aperiodic trajectories and high sensitiveness to small changes of the couplings, or by chaotic trajectories and bifurcation cascades. Quite interestingly, we find out that even a moderate consensus in one single community can remove the chaos. Connections of the model with interacting stock markets are discussed.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 89.65.-s – Social and economic systems
© EPLA, 2014