In this work we study the collective behaviors arising in a model of a simplified homogeneous society. Each agent is modeled as a binary “perceptron”, receiving neighbors’ opinions as inputs and outputting one of two possible opinions, according to the conformist attitude and to the external pressure of mass media. For a neighborhood size greater than three, the system shows a very complex phas...

We characterize the edge of chaos, the boundary which separates initial conditions which lead to chaotic behavior from those which directly decay to the laminar state, for a nine-dimensional shear flow model. This boundary is the eight-dimensional stable manifold of an unstable periodic orbit, whose properties are characterized. Furthermore, we compute the probability that perturbations of a gi...

To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the spiral defect chaos state of a convecting fluid. The simulations show that the transport is diffusive and is enhanced by the spatiotemporal chaos. The enhan...

A numerical study has been done of collisions between protons and hydrogen atoms, treated as classical particles, at low impact velocities. The presence of chaos has been looked for by investigating the processes with standard techniques of the chaotic–scattering theory. The evidence of a sharp transition from nearly regular scattering to fully developed chaos has been found at the lower veloci...

The system of equations introduced by Lorenz to model turbulent convective flow is studied here for Rayleigh numbers r somewhat smaller than the critical value required for sustained chaotic behavior. In this regime the system is found to exhibit transient chaotic behavior. Some statistical properties of this transient chaos are examined numerically. A mean decay time from chaos to steady flow ...

We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on coupling strengths which ensure the stability of synchronized chaos. Previous results in this area involving particular coupling schemes (e.g. global coupling an...

We model an isolated quantum computer as a two-dimensional lattice of qubits (spin halves) with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. In the limit when fluctuations and couplings are small compared to the one-qubit energy spacing, the spectrum has a band structure and we study the quantum computer core (central band) with the highest density o...