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.