ν)⋅sign(x). This is the normal form for splitting the homoclinic loop with additional degeneracy in flows with symmetry that have a saddle equilibrium with a one-dimensional unstable manifold. Due to L. P. Shilnikov' results, such a bifurcation (under certain conditions) corresponds to the birth of the Lorenz attractor. selleck chemicals llc We indicate those regions in the parameter plane where the topological entropy depends monotonically on the parameter c, as well as those for which the monotonicity does not take place. Also, we indicate the corresponding bifurcations for the Lorenz attractors.A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal, for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the underlying system's parameters by measuring its time-evolution only once? The key information for performing this estimation lies in the temporal inter-dependencies between the signal and the model. We propose a kernel-based score to compare these dependencies. Our score generalizes a maximum likelihood estimator for a linear model to a general nonlinear setting in an unknown feature space. We estimate the system's underlying parameters by maximizing the proposed score. We demonstrate the accuracy and efficiency of the method using two chaotic dynamical systems-the double pendulum and the Lorenz '63 model.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). link2 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. link3 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. 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.Second-generation bromodomain and extra terminal (BET) inhibitors, which selectively target one of the two bromodomains in the BET proteins, have begun to emerge in the literature. These inhibitors aim to help determine the roles and functions of each domain and assess whether they can demonstrate an improved safety profile in clinical settings compared to pan-BET inhibitors. Herein, we describe the discovery of a novel BET BD2-selective chemotype using a structure-based drug design from a hit identified by DNA-encoded library technologies, showing a structural differentiation from key previously reported greater than 100-fold BD2-selective chemotypes GSK620, GSK046, and ABBV-744. Following a structure-based hypothesis for the selectivity and optimization of the physicochemical properties of the series, we identified 60 (GSK040), an in vitro ready and in vivo capable BET BD2-inhibitor of unprecedented selectivity (5000-fold) against BET BD1, excellent selectivity against other bromodomains, and good physicochemical properties. This novel chemical probe can be added to the toolbox used in the advancement of epigenetics research.The phase transfer of ions is driven by gradients of chemical potentials rather than concentrations alone (i.e., by both the molecular forces and entropy). Extraction is a combination of high-energy interactions that correspond to short-range forces in the first solvation shell such as ion pairing or complexation forces, with supramolecular and nanoscale organization. While the latter are similar to the long-range solvent-averaged interactions in the colloidal world, in solvent extraction they are associated with lower characteristic lengths of the nanometric domain. Modeling of such complex systems is especially complicated because the two domains are coupled, whereas the resulting free energy of extraction is around kBT to guarantee the reversibility of the practical process. Nevertheless, quantification is possible by considering a partitioning of space among the polar cores, interfacial film, and solvent. The resulting free energy of transfer can be rationalized by utilizing a combination of terms which represent strong complexation energies, counterbalanced by various entropic effects and the confinement of polar solutes in nanodomains dispersed in the diluent, together with interfacial extractant terms. We describe here this ienaics approach in the context of solvent extraction systems; it can also be applied to further complex ionic systems, such as membranes and biological interfaces.
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