Absence of chaos in a self-organized critical coupled map lattice

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Abstract
Although ecologists have been aware for almost 20 years that population densities may evolve in a chaotic way, the evidence for chaos in natural populations is rather poor. The lack of convincing evidence may have its origin in the difficulty of estimating the effect of external environmental noise, but it may also reflect natural regulation processes. In this paper we present a metapopulation-dynamical model, in which the nearest neighbor local population fragments interact by applying a threshold condition. Namely, each local population follows its own temporal evolution until a critical population density is reached, which initiates dispersal (migration) events to the neighbors. The type of interaction is common to self-organized critical cellular automaton models. Depending on the threshold level, the global behavior of our model can be characterized either by noisy dynamics with many degrees of freedom, by a periodical evolution, or by an evolution towards a fixed point. Low dimensional collective chaos does not occur. Moreover, self-organized criticality with power law distributions emerges if the interaction between the neighboring local populations is strong enough.

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