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Whether in search of better trade opportunities or escaping wars, humans have always been on the move. For almost a century, mathematical models of human mobility have been instrumental in the quantification of commuting patterns and migratory fluxes. Equity is a common premise of most of these mathematical models, such that living conditions and job opportunities are assumed to be equivalent across cities. Growing inequalities in modern urban economy and pressing effects of climate change significantly strain this premise. Here, we propose a mobility model that is aware of inequalities across cities in terms of living conditions and job opportunities. Comparing results with real datasets, we show that the proposed model outperforms the state-of-the-art in predicting migration patterns in South Sudan and commuting fluxes in the United States. This model paves the way to critical research on resilience and sustainability of urban systems.

The emergence of collective behaviors in networks of dynamical units in pairwise interaction has been explained as the effect of diffusive coupling. How does the presence of higher-order interaction impact the onset of spontaneous or induced synchronous behavior? Inspired by actuation and measurement constraints typical of physical and engineered systems, we propose a diffusion mechanism over hypergraphs that explains the onset of synchronization through a clarifying analogy with signed graphs. Our findings are mathematically backed by general conditions for convergence to the synchronous state.

Our ability to control network dynamical systems is often hindered by constraints on the number and nature of the available control actions, which make controlling the whole network unfeasible. In this manuscript, we focus on the case where unilateral inputs are exerted on a subset of the network nodes. Leveraging the observation that, different from the case of subsystems, unilateral node reachability and controllability are equivalent, we provide conditions for a given node subset to be unilaterally controllable. The theoretical findings are then employed to develop a computationally efficient heuristic to select the nodes where the unilateral inputs should be injected

This paper deals with adaptive synchronization of chaos in the presence of time-varying communication-delays. We consider two bidirectionally coupled systems that seek to synchronize through a signal that each system sends to the other one and is transmitted with an unknown time-varying delay. We show that an appropriate adaptive strategy can be devised that is successful in dynamically identifying the time-varying delay and in synchronizing the two systems. The performance of our strategy with respect to the choice of the initial conditions and the presence of noise in the communication channels is tested by using numerical simulations. Another advantage of our approach is that in addition to estimating the communication-delay, the adaptive strategy could be used to simultaneously identify other parameters, such as e.g., the unknown time-varying amplitude of the received signal., Comment: Accepted for publication in Chaos, Solitons & Fractals