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The connection adaption strategy (CAS) has been proposed for the synchronization of networked mobile chaotic agents, which is considered to be a simpler scheme compared to commonly used coupling adaption strategies. However, this strategy only provides a limited range of feasible coupling strength allowing a success control. In this paper, we develop the CAS by introducing a jump process to resolve this problem. We show that the proposed approach systematically outperforms the original CAS in the whole range of the mobility and the range of feasible coupling strength is extensively expanded. In addition, we show that motion of the agents could be classified into three different regimes. The dynamical features of these motion regimes are analyzed and relevant measures are provided to characterize the controllability of the network in each regime.

Epidemic spreading processes on multiplex networks have richer dynamical properties than those on single layered networks. To describe the intertwined processes on such networks, heterogeneous mean field (HMF) approach for continuous-time processes and microscopic Markov chain approach for discrete-time processes have been proposed. However, it has been shown that the time evolution of infected individuals and the final epidemic size obtained from these approaches have noticeable discrepancy comparing to those from Monte Carlo simulations. In this paper, we extend the approach of effective degree theory (EDT) on multiplex networks. We will show that predictions obtained from the EDT have excellent agreement with Monte Carlo simulations. Moreover, since the dynamics on multiplex networks involve more dynamical variables, which may invoke more computations, to reduce the computational burden, we further develop an approach based on partial effective degree theory (PEDT) for analyzing the dynamics on multiplex networks, where one layer adopts EDT and the other layer adopts the HMF. Our results show that PEDT has a good performance in predicting the target dynamical process.