We propose a Lévy noise-driven susceptible-exposed-infected-recovered model incorporating media coverage to analyze the outbreak of COVID-19. We conduct a theoretical analysis of the stochastic model by the suitable Lyapunov function, including the existence and uniqueness of the positive solution, the dynamic properties around the disease-free equilibrium and the endemic equilibrium; we deduce a stochastic basic reproduction number R0 s for the extinction of disease, that is, if R0 s≤1, the disease will go to extinction. Particularly, we fit the data from Brazil to predict the trend of the epidemic. Our main findings include the following (i) stochastic perturbation may affect the dynamic behavior of the disease, and larger noise will be more beneficial to control its spread; (ii) strengthening social isolation, increasing the cure rate and media coverage can effectively control the spread of disease. Our results support the feasible ways of containing the outbreak of the epidemic.Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done numerically, the interesting dynamics that have emerged, and the largely unsuccessful attempts that have been made to analytically treat the evolution of densities in differential delay equations. We also present a new approach to the problem and illustrate it with a simple example.Propagation of rays in 2D and 3D corrugated waveguides is performed in the general framework of stability indicators. The analysis of stability is based on the Lyapunov and reversibility error. It is found that the error growth follows a power law for regular orbits and an exponential law for chaotic orbits. A relation with the Shannon channel capacity is devised and an approximate scaling law found for the capacity increase with the corrugation depth.When a disease spreads in a population, individuals tend to change their behavior due to the presence of information about disease prevalence. Therefore, the infection rate is affected and incidence term in the model should be appropriately modified. In addition, a limitation of medical resources has its impact on the dynamics of the disease. In this work, we propose and analyze an Susceptible-Exposed-Infected-Recovered (SEIR) model, which accounts for the information-induced non-monotonic incidence function and saturated treatment function. The model analysis is carried out, and it is found that when R0 is below one, the disease may or may not die out due to the saturated treatment (i.e., a backward bifurcation may exist and cause multi-stability). Further, we note that in this case, disease eradication is possible if medical resources are available for all. When R0 exceeds one, there is a possibility of the existence of multiple endemic equilibria. These multiple equilibria give rise to rich and complex dynamics by showing various bifurcations and oscillations (via Hopf bifurcation). A global asymptotic stability of a unique endemic equilibrium (when it exists) is established under certain conditions. An impact of information is shown and also a sensitivity analysis of model parameters is performed. Various cases are considered numerically to provide the insight of model behavior mathematically and epidemiologically. We found that the model shows hysteresis. Our study underlines that a limitation of medical resources may cause bi(multi)-stability in the model system. Also, information plays a significant role and gives rise to a rich and complex dynamical behavior of the model.Non-smooth systems can generate dynamics and bifurcations that are drastically different from their smooth counterparts. In this paper, we study such homoclinic bifurcations in a piecewise-smooth analytically tractable Lorenz-type system that was recently introduced by Belykh et al. [Chaos 29, 103108 (2019)]. Through a rigorous analysis, we demonstrate that the emergence of sliding motions leads to novel bifurcation scenarios in which bifurcations of unstable homoclinic orbits of a saddle can yield stable limit cycles. These bifurcations are in sharp contrast with their smooth analogs that can generate only unstable (saddle) dynamics. We construct a Poincaré return map that accounts for the presence of sliding motions, thereby rigorously characterizing sliding homoclinic bifurcations that destroy a chaotic Lorenz-type attractor. selleck products In particular, we derive an explicit scaling factor for period-doubling bifurcations associated with sliding multi-loop homoclinic orbits and the formation of a quasi-attractor. Our analytical results lay the foundation for the development of non-classical global bifurcation theory in non-smooth flow systems.Many practical systems can be well described by various fractional-order equations. This paper focuses on identifying the topology of the response layer of a drive-response fractional-order complex dynamical network using the auxiliary-system approach. Specifically, the response layer and the auxiliary layer receive the same input signals from the drive layer. By a designed adaptive control law, the unknown topology of the response layer is successfully identified. Moreover, the proposed method is effective even if the drive layer is made up of isolated nodes. The correctness of the theoretical results is demonstrated by numerical simulations.Two-dimensional materials exhibit properties promising for novel applications. Topologically protected states at their edges can be harnessed for use in quantum devices. We use ab initio simulations to examine properties of edges in 1T'-WTe2 monolayers, known to exhibit topological order, and their interactions with Cu atoms. Comparison of (010)-oriented edges that have the same composition but different terminations shows that, as the number of Cu atoms increases, their thermodynamically preferred arrangement depends on the details of the edge structure. Cu atoms aggregate into a cluster at the most stable edge; while the cluster is nonmagnetic, it spin-polarizes the W atoms along the edge, which removes the topological protection. At the metastable edge, Cu atoms form a chain incorporated into the WTe2 lattice; the topological state is preserved in spite of the dramatic edge restructuring. This suggests that exploiting interactions of metal species with metastable edge terminations can provide a path toward noninvasive interfaces.