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The chaotic pattern of the Hopf-Turing region may be shifted to a spot type pattern of the Turing region depending on the refuge level of the habitat.In this work, we only use data on the unstable manifold to locate the partition boundaries by checking folding points at different levels, which practically coincide with homoclinic tangencies. The method is then applied to the classic two-dimensional Hénon map and a well-known three-dimensional map. Comparison with previous results is made in the Hénon case, and Lyapunov exponents are computed through the metric entropy based on the partition to show the validity of the current scheme.The interplay between interaction, disorder, and dissipation has shown a rich phenomenology. Here, we investigate a disordered XXZ spin chain in contact with a bath which, alone, would drive the system toward a highly delocalized and coherent Dicke state. We show that there exist regimes for which the natural orbitals of the single-particle density matrix of the steady state are all localized in the presence of strong disorders, for either weak interaction or strong interaction. We show that the averaged steady-state occupation in the eigenbasis of the open system Hamiltonian could follow an exponential decay for intermediate disorder strength in the presence of weak interactions, while it is more evenly spread for strong disorder or for stronger interactions. Last, we show that strong dissipation increases the coherence of the steady states, thus reducing the signatures of localization. We capture such signatures of localization also with a concatenated inverse participation ratio that simultaneously takes into account how localized are the eigenstates of the Hamiltonian and how close is the steady state to an incoherent mixture of different energy eigenstates.Identification of influential nodes in complex networks is an area of exciting growth since it can help us to deal with various problems. Furthermore, identifying important nodes can be used across various disciplines, such as disease, sociology, biology, engineering, just to name a few. Hence, how to identify influential nodes more accurately deserves further research. Traditional identification methods usually only focus on the local or global information of the network. However, only focusing on a part of the information in the network will lead to the loss of information, resulting in inaccurate results. In order to address this problem, an identification method based on network efficiency of edge weight updating is proposed, which can effectively incorporate both global and local information of the network. Our proposed method avoids the lack of information in the network and ensures the accuracy of the results as much as possible. Moreover, by introducing the iterative idea of weight updating, some dynamic information is also introduced into our proposed method, which is more convincing. Varieties of experiments have been carried out on 11 real-world data sets to demonstrate the effectiveness and superiority of our proposed method.Geographic tongue or benign migratory glossitis is a condition of an unknown cause characterized by chronic lesions that slowly migrate across the surface of the tongue. The condition's characteristic wavefronts suggest that it can be modeled as a reaction-diffusion system. Here, we present a model for geographic tongue pattern evolution using reaction-diffusion equations applied to portions of spheroids and paraboloids that approximate a tongue shape. We demonstrate that the observed patterns of geographic tongue lesions can be explained by propagating reaction-diffusion waves on these variably curved surfaces.In this work, an epidemiological model is constructed based on a target problem that consists of a chemical reaction on a lattice. We choose the generalized scale-free network to be the underlying lattice. Susceptible individuals become the targets of random walkers (infectious individuals) that are moving over the network. The time behavior of the susceptible individuals' survival is analyzed using parameters like the connectivity γ of the network and the minimum (Kmin) and maximum (Kmax) allowed degrees, which control the influence of social distancing and isolation or spatial restrictions. In all cases, we found power-law behaviors, whose exponents are strongly influenced by the parameter γ and to a lesser extent by Kmax and Kmin, in this order. The number of infected individuals diminished more efficiently by changing the parameter γ, which controls the topology of the scale-free networks. A similar efficiency is also reached by varying Kmax to extremely low values, i.e., the number of contacts of each individual is drastically diminished.We used transition path theory (TPT) to infer "reactive" pathways of floating marine debris trajectories. The TPT analysis was applied on a pollution-aware time-homogeneous Markov chain model constructed from trajectories produced by satellite-tracked undrogued buoys from the National Oceanic and Atmospheric Administration's Global Drifter Program. The latter involved coping with the openness of the system in physical space, which further required an adaptation of the standard TPT setting. Directly connecting pollution sources along coastlines with garbage patches of varied strengths, the unveiled reactive pollution routes represent alternative targets for ocean cleanup efforts. Among our specific findings we highlight constraining a highly probable pollution source for the Great Pacific garbage patch; characterizing the weakness of the Indian Ocean gyre as a trap for plastic waste; and unveiling a tendency of the subtropical gyres to export garbage toward the coastlines rather than to other gyres in the event of anomalously intense winds.We generalize the study of the noisy Kuramoto model, considered on a network of two interacting communities, to the case where the interaction strengths within and across communities are taken to be different in general. By developing a geometric interpretation of the self-consistency equations, we are able to separate the parameter space into ten regions in which we identify the maximum number of solutions in the steady state. Furthermore, we prove that in the steady state, only the angles 0 and π are possible between the average phases of the two communities and derive the solution boundary for the unsynchronized solution. Last, we identify the equivalence class relation in the parameter space corresponding to the symmetrically synchronized solution.Machine learning techniques have been witnessing perpetual success in predicting and understanding behaviors of a diverse range of complex systems. By employing a deep learning method on limited time-series information of a handful of nodes from large-size complex systems, we label the underlying network structures assigned in different classes. We consider two popular models, namely, coupled Kuramoto oscillators and susceptible-infectious-susceptible to demonstrate our results. Importantly, we elucidate that even binary information of the time evolution behavior of a few coupled units (nodes) yields as accurate classification of the underlying network structure as achieved by the actual time-series data. The key of the entire process reckons on feeding the time-series information of the nodes when the system evolves in a partially synchronized state, i.e., neither completely incoherent nor completely synchronized. The two biggest advantages of our method over previous existing methods are its simplicity and the requirement of the time evolution of one largest degree node or a handful of the nodes to predict the classification of large-size networks with remarkable accuracy.Complex canard-type oscillatory regimes in stochastically forced flows of suspensions are studied. In this paper, we use the nonlinear dynamical model with a N-shaped rheological curve. Amplitude and frequency characteristics of self-oscillations in the zone of canard explosion are studied in dependence on the stiffness of this N-shaped function. [https://www.selleckchem.com/products/pyrrolidinedithiocarbamate-ammoniumammonium.html Pyrrolidinedithiocarbamate ammonium chemical structure] A constructive role of random noise in the formation of complex oscillatory regimes is investigated. A phenomenon of the noise-induced splitting of stochastic cycles is discovered and studied both numerically and analytically by the stochastic sensitivity technique. Supersensitive canard cycles are described and their role in noise-induced transitions from order to chaos is discussed.In the field of complex systems, it is often possible to arrive at some simple stochastic or chaotic Low Order Models (LOMs) exploiting the time scale separation between leading modes of interest and fast fluctuations. These LOMs, although approximate, might provide interesting qualitative insights regarding some important aspects like the average time between two extreme events. Recently, the simplest example of a LOM with multiplicative noise, namely, a linear system with a linearly state dependent noise [also called correlated additive and multiplicative (CAM) model], has been considered as archetypal for numerous phenomena that present markedly non-Gaussian statistics. We show in this paper that the determination of the parameters of a CAM model from the (few) available data is far from trivial and that the actual most likely parameters might differ substantially from the ones determined directly from a (necessarily limited) short sequence of observations. We illustrate how this problem can be tackled, at least to the extent possible, using an approach that is based on Bayes' theorem. We shall focus on a CAM modeling the El Niño Southern Oscillation but the methodology can be extended to any phenomenon that can be described by a simplified LOM similar to the one examined here and where the available sequence of data is relatively short. We conclude that indeed a Bayesian approach can fix the problem.We suggest a theoretical framework to study the dynamics of an open city, with cars entering at a certain rate and leaving as they reach their destinations. In particular, we assess through simulations some unexpected consequences of the massive use of GPS (global positioning system) navigation systems in the overall dynamics. One of our main interest is to identify what type of measurements would be the most relevant for an experimental study of this system, specifically, the ones useful for city traffic administrators. To do so, we solve the microdynamics using a cellular automaton model considering three different navigation strategies based on the minimization of the individual paths (unweighted strategy) or travel times (weighted strategies). Although the system is inherently stochastic, we found in our simulations an equivalent saddle-node bifurcation for all strategies where the input rate acts as a bifurcation parameter. There is also evidence of additional bifurcations for travel time minimization based strategies. Although we found that weighted strategies are more efficient in terms of car motion, there is a destabilization phenomenon that makes, in an unexpected way, a variation of the unweighted strategy more optimal at certain densities from the fuel efficiency of the overall city traffic point of view. These results bring new insight into the intrinsic dynamics of cities and the perturbations that individual traffic routing can produce on the city as a whole.