Strange attractors in coupled reaction-diffusion cells

Abstract

A numerical study of two identical reaction cells with diffusion coupling has shown that the structure of motion in the system in principle agrees with results reported for variety of dynamic systems. When the characteristic parameter is varied, alternating sub-intervals of stable periodic ( P k ) and stable aperiodic ( A l ) solutions appear. The sub-intervals are connected by intervals, where tangent bifurcations and infinite sequences of subharmonic bifurcations occur. Feigenbaum relation holds for the studied sequence of subharmonic bifurcations. Aperiodic (chaotic) states are characterized by a complete set of one-dimensional Lyapunov exponents, by power spectra, and by corresponding Poincaré maps. The spectra of Lyapunov exponents are of the type (+.0.-.-), and show that the topological dimension of the chaotic attractor is two. The power spectra are of two different types (a) the spectra with sharp peaks located above the broad-band noise, showing statistical phase coherence of the attractor, (b) the flat spectra showing only broad-band noise, corresponding to phase incoherent attractor. The phase coherence is present close after every point of accumulation. Phase incoherence arises when the strange attractors contain unstable periodic orbits with different topology. The relations of bifurcated stable and unstable periodic solutions (computed by means of continuation techniques) to the structure of the strange attractor is discussed and Poincaré maps are used to illustrate the dependence of the structure of the attractors on the value of the characteristic parameter.