Coupled systems can exhibit an unusual kind of multistability, namely, the coexistence of infinitely many attractors for a given set of parameters. This extreme multistability is demonstrated to occur in coupled chemical model systems with various types of coupling. We show that the appearance of extreme multistability is associated with the emergence of a conserved quantity in the long-term limit. This conserved quantity leads to a “slicing” of the state space into manifolds corresponding to the value of the conserved quantity. The state space “slices” develop as $t\to \infty$ and there exists at least one attractor in each of them. We discuss the dependence of extreme multistability on the coupling and on the mismatch of parameters of the coupled systems.

• Received 2 November 2010

DOI:https://doi.org/10.1103/PhysRevE.83.056206