Chaos: An Interdisciplinary Journal of Nonlinear Science is a peerreviewed journal devoted to increasing the understanding of nonlinear phenomena. Chaos is committed to publish selective and high quality content that is accessible to researchers from a broad spectrum of disciplines. Topics cover nonlinear dynamical systems, neural networks and neurodynamics, climate and earth sciences, condensed matter, fluid dynamics, synchronization, turbulence, solitons and coherent structures, timeseries analysis, and more.
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Dynamical systems are frequently used to model biological systems. When these models are fit to data, it is necessary to ascertain the uncertainty in the model fit. Here, we present prediction deviation, a metric of uncertainty that determines the extent to which observed data have constrained the model's predictions. This is accomplished by solving an optimization problem that searches for a pair of models that each provides a good fit for the observed data, yet has maximally different predictions. We develop a method for estimating a priori the impact that additional experiments would have on the prediction deviation, allowing the experimenter to design a set of experiments that would most reduce uncertainty. We use prediction deviation to assess uncertainty in a model of interferonalpha inhibition of viral infection, and to select a sequence of experiments that reduces this uncertainty. Finally, we prove a theoretical result which shows that prediction deviation provides bounds on the trajectories of the underlying true model. These results show that prediction deviation is a meaningful metric of uncertainty that can be used for optimal experimental design.

We report on the first demonstration of chaosassisted directed transport of a quantum particle held in an amplitudemodulated and tilted optical lattice, through a resonanceinduced doublemean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaosassisted transport feature can be verified experimentally by using a source of single atoms to detect the doublemean displacement one by one, and can be extended to different scientific fields.

The paper describes the results of study of a system of coupled nonlinear, Duffingtype oscillators, from the viewpoint of their selfsynchronization, i.e., generation of a coherent field (order parameter) via instability of an incoherent (randomphase) initial state. We consider both the cases of dissipative coupling (e.g., via the joint radiation) and reactive coupling in a Hamiltonian system.

It is well known that line graphs offer a good summary of the graphs properties, which make them easier to analyze and highlight the desired properties. We extend the concept of line graph to multiplex networks in order to analyze multiplexed and multilayered networked systems. As these structures are very rich, different approaches to this notion are required to capture a variety of situations. Some relationships between these approaches are established. Finally, by means of some simulations, the potential utility of this concept is illustrated.

Explosive synchronization has recently been reported in a system of adaptively coupled Kuramoto oscillators, without any conditions on the frequency or degree of the nodes. Here, we find that, in fact, the explosive phase coexists with the standard phase of the Kuramoto oscillators. We determine this by extending the meanfield theory of adaptively coupled oscillators with full coupling to the case with partial coupling of a fraction f. This analysis shows that a metastable region exists for all finite values of f > 0, and therefore explosive synchronization is expected for any perturbation of adaptively coupling added to the standard Kuramoto model. We verify this theory with GPUaccelerated simulations on very large networks (N ∼ 10^{6}) and find that, in fact, an explosive transition with hysteresis is observed for all finite couplings. By demonstrating that explosive transitions coexist with standard transitions in the limit of f → 0, we show that this behavior is far more likely to occur naturally than was previously believed.