Transition from regularity to Li-Yorke chaos in coupled logistic networks

The transition from regularity to chaos in the sense of Li-Yorke is investigated in this Letter. A logistic network is investigated in detail, where all nodes in the network are the same logistic maps in non-chaotic states (with the parameter μ in non-chaotic regions). It is proved that when μ>1, these non-chaotic logistic nodes can become chaotic in the sense of Li-Yorke. Extensive simulations lead to the conjecture that when μ⩽1 such a logistic network is “super-stable”, because no matter how strong the coupling strength is, the network does not transfer to a chaotic state.