We investigate the Z(2) gauge model on a generalized Bethe lattice in the presence of a three-plaquette interaction. We obtain a cascade of phase transitions according to the Feigenbaum scheme leading to chaotic states for some values of parameters of the model. The duality between this gauge model and the three-site Ising spin model on the Husimi tree is shown. The Lyapunov exponents as new or...

Here it is shown that chaotic oscillations can appear after a series of period doublings in radiating diffusion flames when the activation temperature is high enough. It is also shown that period doubling cascades appear typically in very small regions and that they may not be observable if one starts with small perturbations of a steady flame.