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In this study, an extended spatiotemporal model of a human immunodeficiency virus (HIV) CD4+ T cell with a drug therapy effect is proposed for the numerical investigation. The stability analysis of equilibrium points is carried out for temporal and spatiotemporal cases where stability regions in the space of parameters for each case are acquired. Three numerical techniques are used for the numerical simulations of the proposed HIV reaction-diffusion system. These techniques are the backward Euler, Crank-Nicolson, and a proposed structure preserving an implicit technique. The proposed numerical method sustains all the important characteristics of the proposed HIV model such as positivity of the solution and stability of equilibria, whereas the other two methods have failed to do so. We also prove that the proposed technique is positive, consistent, and Von Neumann stable. The effect of different values for the parameters is investigated through numerical simulations by using the proposed method. The stability of the proposed model of the HIV CD4+ T cell with the drug therapy effect is also analyzed.We present a hybrid framework appropriate for identifying distinct dynamical regimes and transitions in a paleoclimate time series. [https://www.selleckchem.com/products/wnt-c59-c59.html selleck] Our framework combines three powerful techniques used independently of each other in time series analysis a recurrence plot, manifold learning through Laplacian eigenmaps, and Fisher information metric. The resulting hybrid approach achieves a more automated classification and visualization of dynamical regimes and transitions, including in the presence of missing values, observational noise, and short time series. We illustrate the capabilities of the method through several pragmatic numerical examples. Furthermore, to demonstrate the practical usefulness of the method, we apply it to a recently published paleoclimate dataset a speleothem oxygen isotope record from North India covering the past 5700 years. This record encodes the patterns of monsoon rainfall over the region and covers the critically important period during which the Indus Valley Civilization matured and declined. We identify a transition in monsoon dynamics, indicating a possible connection between climate change and the decline of the Indus Valley Civilization.A ring resonator made of a silica-based optical fiber is a paradigmatic system for the generation of dissipative localized structures or dissipative solitons. We analyze the effect of the non-instantaneous nonlinear response of the fused silica or the Raman response on the formation of localized structures. After reducing the generalized Lugiato-Lefever to a simple and generic bistable model with a nonlocal Raman effect, we investigate analytically the formation of moving temporal localized structures. This reduction is valid close to the nascent bistability regime, where the system undergoes a second-order critical point marking the onset of a hysteresis loop. The interaction between fronts allows for the stabilization of temporal localized structures. Without the Raman effect, moving temporal localized structures do not exist, as shown in M. G. Clerc, S. Coulibaly, and M. Tlidi, Phys. Rev. Res. 2, 013024 (2020). The detailed derivation of the speed and the width associated with these structures is presented. We characterize numerically in detail the bifurcation structure and stability associated with the moving temporal localized states. The numerical results of the governing equations are in close agreement with analytical predictions.The observable outputs of many complex dynamical systems consist of time series exhibiting autocorrelation functions of great diversity of behaviors, including long-range power-law autocorrelation functions, as a signature of interactions operating at many temporal or spatial scales. Often, numerical algorithms able to generate correlated noises reproducing the properties of real time series are used to study and characterize such systems. Typically, many of those algorithms produce a Gaussian time series. However, the real, experimentally observed time series are often non-Gaussian and may follow distributions with a diversity of behaviors concerning the support, the symmetry, or the tail properties. It is always possible to transform a correlated Gaussian time series into a time series with a different marginal distribution, but the question is how this transformation affects the behavior of the autocorrelation function. Here, we study analytically and numerically how the Pearson's correlation of two Gaussiicking the marginal distribution and the power-law tail of the autocorrelation function of real time series the absolute returns of stock prices.We use statistical tools to characterize the response of an excitable system to periodic perturbations. The system is an optically injected semiconductor laser under pulsed perturbations of the phase of the injected field. We characterize the laser response by counting the number of pulses emitted by the laser, within a time interval, ΔT, that starts when a perturbation is applied. The success rate, SR(ΔT), is then defined as the number of pulses emitted in the interval ΔT, relative to the number of perturbations. The analysis of the variation of SR with ΔT allows separating a constant lag of technical origin and a frequency-dependent lag of physical and dynamical origin. Once the lag is accounted for, the success rate clearly captures locked and unlocked regimes and the transitions between them. We anticipate that the success rate will be a practical tool for analyzing the output of periodically forced systems, particularly when very regular oscillations need to be generated via small periodic perturbations.The double excitation multi-stability and Shilnikov-type multi-pulse jumping chaotic vibrations are analyzed for the bistable asymmetric laminated composite square panel under foundation force for the first time. Based on the extended new high-dimensional Melnikov function, the explicit sufficient conditions are obtained for the existence of the Shilnikov-type multi-pulse jumping homoclinic orbits and chaotic vibrations in the bistable asymmetric laminated composite square panel, which implies that multi-pulse jumping chaotic vibrations may occur in the sense of Smale horseshoes. The extended new high-dimensional Melnikov function gives the parameters domain of the intersection for the homoclinic orbits, which illustrates the relationship among the coefficients of damping, parametric, and external excitations. Numerical simulations including the bifurcation diagrams, largest Lyapunov exponents, phase portraits, waveforms, and Poincaré sections are utilized to study the double excitation multi-pulse jumping and metastable chaotic vibrations and dynamic snap-through phenomena.