Criticality and Chaos in Systems of Communities

8th Brazilian Meeting on Simulational Physics

Ostilli, Massimo^1 ; Figueiredo, Wagner^1

Departamento de Fisica, Universidade Federal de Santa Catarina, Florianopolis

SC

88040-900, Brazil^1

关键词: Discrete time dynamics;    Dynamical instabilities;    Local time;    Lyapunov exponent;    Simple modeling;    Thermal equilibriums;    Time interval;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/686/1/012006/pdf
DOI  :  10.1088/1742-6596/686/1/012006

来源: IOP

【 摘 要 】

We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a Glauber-like dynamics. We analyze and compare four different versions of the dynamics: flow (differential equations), map (discretetime dynamics), local-time update flow, and local-time update map. The presence of only bilinear interactions prevent the flow cases to develop any dynamical instability, the system converging always to the thermal equilibrium. The situation is different for the map when unfriendly couplings are involved, where period-two oscillations arise. In the case of the map with local-time updates, oscillations of any period and chaos can arise as a consequence of the reciprocal "tension" accumulated among the communities during their sleeping time interval. The resulting chaos can be of two kinds: true chaos characterized by positive Lyapunov exponent and bifurcation cascades, or marginal chaos characterized by zero Lyapunov exponent and critical continuous regions.