dynamical system
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Abstract In a recent study by Wang et al. (2021a) that introduced a dynamical efficiency to the intensification potential of a tropical cyclone (TC) system, a simplified energetically based dynamical system (EBDS) model was shown to be able to capture the intensity-dependence of TC potential intensification rate (PIR) in both idealized numerical simulations and observations. Although the EBDS model can capture the intensity-dependence of TC intensification as in observations, a detailed evaluation has not yet been done. This study provides an evaluation of the EBDS model in reproducing the intensity-dependent feature of the observed TC PIR based on the best-track data for TCs over the North Atlantic, central, eastern and western North Pacific during 1982–2019. Results show that the theoretical PIR estimated by the EBDS model can capture basic features of the observed PIR reasonably well. The TC PIR in the best-track data increases with increasing relative TC intensity (intensity normalized by its corresponding maximum potential intensity–MPI) and reaches a maximum at an intermediate relative intensity around 0.6, and then decreases with increasing relative intensity to zero as the TC approaches its MPI, as in idealized numerical simulations. Results also show that the PIR for a given relative intensity increases with the increasing MPI and thus increasing sea surface temperature, which is also consistent with the theoretical PIR implied by the EBDS model. In addition, future directions to include environmental effects and make the EBDS model applicable to predict intensity change of real TCs are also discussed.

Abstract Nonlinear evolution equations (NLEEs) are extensively used to establish the elementary propositions of natural circumstances. In this work, we study the Konopelchenko-Dubrovsky (KD) equation which depicts non-linear waves in mathematical physics with weak dispersion. The considered model is investigated using the combination of generalized exponential rational function (GERF) method and dynamical system method. The GERF method is utilized to generate closedform invariant solutions to the (2+1)-dimensional KD model in terms of trigonometric, hyperbolic, and exponential forms with the assistance of symbolic computations. Moreover, three-dimensional graphics are displayed to depict the behavior of obtained solitary wave solutions. The model is observed to have single and multiple soliton profiles, kink-wave profiles, and periodic oscillating nonlinear waves. These generated solutions have never been published in the literature. All the newly generated soliton solutions are checked by putting them back into the associated system with the soft computation via Wolfram Mathematica. Moreover, the system is converted into a planer dynamical system using a certain transformation and the analysis of bifurcation is examined. Furthermore, the quasi-periodic solution is investigated numerically for the perturbed system by inserting definite periodic forces into the considered model. With regard to the parameter of the perturbed model, two-dimensional and three-dimensional phase portraits are plotted.

<abstract><p>Public opinion and opinion dynamics can have a strong effect on the transmission rate of an infectious disease for which there is no vaccine. The coupling of disease and opinion dynamics however, creates a dynamical system that is complex and poorly understood. We present a simple model in which susceptible groups adopt or give up prophylactic behaviour in accordance with the influence related to pro- and con-prophylactic communication. This influence varies with disease prevalence. We observe how the speed of the opinion dynamics affects the total size and peak size of the epidemic. We find that more reactive populations will experience a lower peak epidemic size, but possibly a larger final size and more epidemic waves, and that an increase in polarization results in a larger epidemic.</p></abstract>

AbstractIn this paper, we propose an extension of the Ricci-inverse gravity, which has been proposed recently as a very novel type of fourth-order gravity, by introducing a second order term of the so-called anticurvature scalar as a correction. The main purpose of this paper is that we would like to see whether the extended Ricci-inverse gravity model admits the homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker metric as its stable inflationary solution. However, a no-go theorem for inflation in this extended Ricci-inverse gravity is shown to appear through a stability analysis based on the dynamical system method. As a result, this no-go theorem implies that it is impossible to have such stable inflation in this extended Ricci-inverse gravity model.