Chaos, Solitons and Fractals: X最新文献

This paper considers the fractional-order system in the sense of $\psi$-Hilfer fractional differential equations. In order to investigate the existence and uniqueness of the mild solution, the Banach contraction mapping principle and the measure of non-compactness are applied. As an application, the financial crisis model in the sense of $\psi$-Hilfer fractional differential equation will be used to prove the existence of solution and global stability of it. In addition, to illustrate the feasibility and validity of our results, the numerical simulation of the financial crisis model in the sense of Caputo will be shown in four different cases. Our results indicate that for non-integer order, the system behaves to be asymptotically stable and periodic (chaotic) at a certain limit order and the other part stabilizes to a fixed point.

This paper mainly focuses on the issue of finite-time synchronization of a class of chaotic master and slave systems when they have uncertainties, disturbances, and unknown parameters. It is supposed that Uncertainties and disturbances bounds are unknown. First, using the concept of fractional calculus, a new fractional sliding surface is proposed and its finite-time convergence is also proved. Second, appropriate adaptive laws are introduced to overcome unknown system parameters and these laws correctly estimate the unknown values. With applying the controller, synchronization is achieved within a short time. Also after the synchronization, unstable fluctuations are removed and the controlled system has perfect robustness. The proposed approach is applicable to a wide range of identical or non-identical chaotic master and slave systems. Theoretical analysis and stability examination of the proposed method have been performed utilizing adaptive methods and Lyapunov stability theorem. Thereafter, two practical examples are presented to evaluate the effectiveness and usefulness of the suggested method. Furthermore, this method is compared with methods in recent articles, which shows the superiority of this method.

This work deals with the inverse problem in epidemiology based on a SIR model with time-dependent infectivity and recovery rates, allowing for a better prediction of the long term evolution of a pandemic. The method is used for investigating the COVID-19 spread by first solving an inverse problem for estimating the infectivity and recovery rates from real data. Then, the estimated rates are used to compute the evolution of the disease. The time-depended parameters are estimated for the World and several countries (The United States of America, Canada, Italy, France, Germany, Sweden, Russia, Brazil, Bulgaria, Japan, South Korea, New Zealand) and used for investigating the COVID-19 spread in these countries.

When the novel coronavirus disease SARS-CoV2 (COVID-19) was officially declared a pandemic by the WHO in March 2020, the scientific community had already braced up in the effort of making sense of the fast-growing wealth of data gathered by national authorities all over the world. However, despite the diversity of novel theoretical approaches and the comprehensiveness of many widely established models, the official figures that recount the course of the outbreak still sketch a largely elusive and intimidating picture. Here we show unambiguously that the dynamics of the COVID-19 outbreak belongs to the simple universality class of the SIR model and extensions thereof. Our analysis naturally leads us to establish that there exists a fundamental limitation to any theoretical approach, namely the unpredictable non-stationarity of the testing frames behind the reported figures. However, we show how such bias can be quantified self-consistently and employed to mine useful and accurate information from the data. In particular, we describe how the time evolution of the reporting rates controls the occurrence of the apparent epidemic peak, which typically follows the true one in countries that were not vigorous enough in their testing at the onset of the outbreak. The importance of testing early and resolutely appears as a natural corollary of our analysis, as countries that tested massively at the start clearly had their true peak earlier and less deaths overall.

In a quantum gravity environment, the processes and events are causally non-separable because the term of time and the time-steps have no interpretable meaning in a non-fixed causality structure. Here, we study the energy transfer and thermodynamics of quantum gravity computations. We show that a non-fixed causality stimulates entropy transfer between the quantum gravity environment and the independent local systems of the quantum gravity space. We prove that the entropy transfer reduces the entropies of the contributing local systems and increases the entropy of the quantum gravity environment. We reveal on a smooth Cauchy slice that the space-time geometry of the quantum gravity environment dynamically adapts to the vanishing causality. We define the corresponding Hamiltonians and the causal development of the quantum gravity environment.

We quantify how incorporating physics into neural network design can significantly improve the learning and forecasting of dynamical systems, even nonlinear systems of many dimensions. We train conventional and Hamiltonian neural networks on increasingly difficult dynamical systems and compute their forecasting errors as the number of training data and number of system dimensions vary. A map-building perspective elucidates the superiority of Hamiltonian neural networks. The results clarify the critical relation among data, dimension, and neural network learning performance.

The construction of a continuous family of distributions on a compact set is demonstrated by concatenating, in a continuous manner, three probability density functions with bounded support using a modified mixture technique. The construction technique is similar to that of generalized trapezoidal (GT) distributions, but contrary to GT distributions, the resulting density function is smooth within its bounded domain. The construction of Generalized Trapezoidal Ogive (GTO) distributions was motivated by the COVID-19 epidemic, where smoothness of an infection rate curve may be a desirable property combined with the ability to separately model three stages and their durations as the epidemic progresses, being: (1) an increasing infection rate stage, (2) an infection rate stage of some stability and (3) a decreasing infection rate stage. The resulting model allows for asymmetry of the infection rate curve opposite to, for example, the Gaussian Error Infection (GEI) rate curve utilized early on for COVID-19 epidemic projections by the Institute for Health Metrics and Evaluation (IHME). While other asymmetric distributions too allow for the modeling of asymmetry, the ability to separately model the above three stages of an epidemic’s progression is a distinct feature of the model proposed. The latter avoids unrealistic projections of an epidemic’s right-tail in the absence of right tail data, which is an artifact of any fatality rate model where a left-tail fit determines its right-tail behavior.