We investigate the collective behavior of a system of chaotic Rossler oscillators indirectly coupled through a common environment that possesses its own dynamics and which in turn is modulated by the interaction with the oscillators. By varying the parameter representing the coupling strength between the oscillators and the environment, we find two collective states previously not reported in systems with environmental coupling; (i) non-trivial collective behavior, characterized by a periodic evolution of macroscopic variables coexisting with the local chaotic dynamics; and (ii) dynamical clustering, consisting of the formation of differentiated subsets of synchronized elements within the system. These states are relevant for many physical and biological systems where interactions with a dynamical environment are frequent.
Many works study the integrability of the Bianchi class A cosmologies with k = 1, where k is the ratio between the pressure and the energy density of the matter. Here we characterize the analytic integrability of the Bianchi class A cosmological models when 0 ¿ k < 1. We conclude that Bianchi types VI0, VII0, VIII and IX can exhibit chaos whereas Bianchi type I is not chaotic and Bianchi type II is at most partially chaotic.
The dynamics of the Lorenz model of general circulation of the atmosphere is investigated. The attractors found are characterized by calculating their Fourier spectra, Lyapunov exponents and dimensions. In addition, the self similarity of the attractors is studied with the aid of a Poincarémap. A series of one-dimensional maps derived from the Poincarésection illustrates the structural changes of the attractors as a function of parameters variations.