In this article, a new method, which constructs a coupling scheme with cooperative and competitive weight-couplings, is used to stabilize arbitrarily selected cluster synchronization patterns with several clusters for connected chaotic networks. By the coupling scheme, a sufficient condition about the global stability of the selected cluster synchronization patterns is derived. That is to say, when the sufficient condition is satisfied, arbitrarily selected cluster synchronization patterns in connected chaotic networks can be achieved via an appropriate coupled scheme. The effectiveness of the method is illustrated by an example.

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We present a morphological classification of 14,245 radio active galactic nuclei (AGNs) into six types, i.e., typical Fanaroff-Riley Class I / II (FRI/II), FRI/II-like bent-tailed, X-shaped radio galaxy, and ringlike radio galaxy, by designing a convolutional neural network (CNN) based autoencoder, namely MCRGNet, and applying it to a labeled radio galaxy (LRG) sample containing 1442 AGNs and an unlabeled radio galaxy (unLRG) sample containing 14,245 unlabeled AGNs selected from the Best-Heckman sample. We train MCRGNet and implement the classification task by a three-step strategy, i.e., pre-training, fine-tuning, and classification, which combines both unsupervised and supervised learnings. A four-layer dichotomous tree is designed to classify the radio AGNs, which leads to a significantly better performance than the direct six-type classification. On the LRG sample, our MCRGNet achieves a total precision of ∼ 93% and an averaged sensitivity of ∼ 87%, which are better than those obtained in previous works. On the unLRG sample, whose labels have been human-inspected, the neural network achieves a total precision of ∼ 80%. Also, using the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) to calculate the r-band absolute magnitude (M opt ) and using the flux densities to calculate the radio luminosity (L radio ), we find that the distributions of the unLRG sources on the L radio -M opt plane do not show an apparent redshift evolution and could confirm with a sufficiently large sample that there could not exist an abrupt separation between FRIs and FRIIs as reported in some previous works.

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