Heteroclinic turbulence in the Lotka-Volterra reaction diffusion equation

Heteroclinic turbulence in the Lotka-Volterra reaction diffusion equation is studied numerically and theoretically, and the statistical, feature is analyzed precisely in reference to the onset mechanism of the turbulence. First, the bifurcation diagram is demonstrated in detail, and a variety of attractors are discussed. It is emphasized that the diversity of the attractor enhances when the system size increases. Next, the transition from a regular attractor to a turbulent one is characterized by a correlation function, as well as by the Lyapunov exponent, where one can observe the scaling laws clearly for the correlation length and the maximum Lyapunov exponent.