Chaos, Solitons and Fractals: X最新文献

The grey prediction model has been widely used in various fields and demonstrated good performance. However, when the data shows non-homogeneous exponential characteristic, the effect of the grey prediction model performs poorly. Therefore, a grey prediction model with a quadratic polynomial term (denoted as NGM(1,1,$k^2$) is developed. The NGM(1,1,$k^2$) model is generalized, the GM(1,1) model, the GM(1,1,k) model, the SAIGM model and the GM(1,1,$k^2$) model are the special forms of it. Moreover, the parameter characteristics of the NGM(1,1,$k^2$) model and the effect on the modeling precision are evaluated under the multiplication transformation. To make the NGM(1,1,$k^2$) model more precise, we further analyze the error of the NGM(1,1,$k^2$) model and propose a new model, named BNGM(1,1,$k^2$) model, of which the background value is reconstructed based on the Simpson formula. Subsequently, the effectiveness of the new model is verified through four cases. The result shows that the prediction accuracy of the BNGM(1,1,$k^2$) model is significantly improved. Finally, the BNGM(1,1,$k^2$) model is applied to analyse and predict the Gross Domestic Product (GDP) of Chongqing’s primary industry, the total power of Chongqing’s agricultural machinery and the GDP of Chongqing’s wholesale and retail trades, which shows the prediction performance of the new model is superior to other models.

Various encryption techniques, mostly based on mathematical and logical principles, are used for protecting sensitive data from attacks meant to modify or unauthorizedly distribute them. The importance of these techniques has grown significantly as various real-life applications in fields like medicine, banking, or transport are accompanied by increasing security concerns. Various effective cryptography schemes were proposed so far in the literature; however, each of them exhibits certain flaws and limitations with respect to different vital aspects. To overcome these issues, we propose a hybrid scheme for securing digital images by encrypting them using a dual security approach. More precisely, we use first a chaotic map for scrambling the image pixels, and then, we apply the singular-value decomposition method for decomposing the permuted image to provide very strong security. Individually each of these steps has already been considered in the cryptographic literature; however, their combination has not been proposed before this contribution. Experimental results on benchmark data validate our proposed scheme and various performance evaluation metrics indicate that it shows promising qualities in terms of security (against various attacks) and sensitivity in comparison with baseline methods.

In this paper, the resonance behavior of a spring-block model with fractional-order derivative under periodic stress perturbation is investigated. Using the harmonic balance method, we derive the frequency-response equations for the system consisting of two blocks linked by a linear spring. The results have shown that the fractional-order derivative and perturbation parameter can affect the dynamical properties of fault rock, which is characterized by the equivalent linear damping coefficient and the equivalent linear stiffness coefficient. The frequency-response curve displays the resonance peaks and one anti-resonance. The effects of parameters $q,{\beta }_0,{\epsilon }_0,{\beta }_1$ and ${\epsilon }_1$ on the resonance and anti-resonance periods and the response amplitudes at the resonance frequency are analyzed. The shear stress response shows that the system accumulates a lot of energy at the resonance frequency. This accumulation can lead to the destabilization of the fault system. The blocks move without accumulating energy at the anti-resonance frequency. This can lead to the stabilization of the fault system.

The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete classification of the systems bifurcations, in particular, a complete analysis on local stability and codimension 1 bifurcations in the parameter space. Sufficient conditions for positive trajectories are given. The existence of a 3-cycle is shown, which implies the existence of cycles of arbitrary length by the celebrated Sharkovskii’s theorem. Generacity of some bifurcations is examined both analytically and through numerical computations. Bifurcation diagrams along with numerical simulations are presented. The system turns out to have both rich and interesting dynamics.

Researchers have identified numerous mechanisms that make cooperation in the prisoner's dilemma possible, yet recent research has proposed what ranks among the most basic of mechanisms: the presence of time. When organisms in spatial models can interact at multiple points in time within a generation, cooperation can evolve in a wider range of settings than in spatial models in which interaction occurs at a single moment. Here we further explore this mechanism via an analytic model that studies the effect of time on cooperation when no spatial dimension is present. The model shows that the mere presence of two or more points in time at which social interaction can occur creates an opportunity for mutant cooperators to invade a well-mixed population of defectors playing the one-shot prisoner's dilemma under the replicator dynamics. These invasions lead to a nonequilbrium cycling of strategies in which cooperation consistently reemerges at alternating time points.

In near-term quantum computers, the computations are realized via unitary operators. The optimization problem fed into the quantum computer sets an objective function that is to be estimated via several measurement rounds. Here, we define a procedure for objective function approximation in gate-model quantum computers. The proposed solution optimizes the process of objective function estimation for optimization problems in gate-model quantum computers and quantum devices.

In this work, we propose a strategy based on an analog active network to detect Hopf bifurcations in two–dimensional dynamical systems described by ordinary differential equations. With the proposed strategy, two parameters of the nonlinear system are established in the analog active network by using external controllable voltage levels in order to explore the dynamical evolution of the system in a fast, easy, and accessible way, making our approach a powerful tool to detect Hopf bifurcations in a two-dimensional space. To demonstrate the proposed strategy’s potential and functionality, we electronically implement the kinetics of a reaction-diffusion model proposed by Barrio et al. in 1999 [1], called BVAM model. Hopf bifurcations are detected by following the changes in the system, going from stationary to periodic solutions when varying the control parameters. Local linear stability analysis is performed to show the quantitative agreement between analytical and experimental bifurcations. We additionally found that global effects are detected by the experimental approach, which cannot be predicted from a local analysis. The proposed strategy opens the way to use analog active networks to detect bifurcations in dynamical systems experimentally.

Based on the characteristic of the COVID-19 asymptomatic infection, and due to the shortage of traditional mathematical models of transmission dynamics of infectious diseases, we propose a new SAIR model. This SAIR model fully considers the infectious characteristics of asymptomatic cases and the transformation characteristics between the four kinds case. According to the data released by the National Health Commission of P.R.C, the model parameters are calculated, and the transmission process of the COVID-19 is simulated dynamically. It is found that the SAIR model data are in good agreement with the actual data, and the time characteristics of the infection rate are particularly accurate, proving the accuracy and effectiveness of the model. Then, on the basis of the differences between the model data and the real data, the standard deviation of the error is calculated. From the standard deviation, the functional intervals of the confirmed infection rate and the asymptomatic infection rate, the interval of the total number of cases in the model, and the interval of the number of asymptomatic cases in the society are also calculated. The number of asymptomatic cases in society is of important and realistic significance for the assessment of risk and subsequent control measures. Then, according to the dynamic simulation data of the model with changed value of parameters, the remarkable effects of strict quarantines are discussed. Finally, the possible direction of further study is given.

The 2019 novel coronavirus disease (COVID-19) has spread rapidly to many countries around the world from Wuhan, the capital of China’s Hubei province since December 2019. It has now a huge effect on the global economy. As of 13 September 2020, more than 28, 802, 775, and 920, 931 people are infected and dead, respectively. The mortality of COVID-19 infections is increasing as the number of infections increase. Many countries published control measures to contain its spread. Even though there are many drugs and vaccines under trial by pharmaceutical companies and research groups, no specific vaccine or drug has yet been found. Therefore, it is necessary to explain the behaviour of the case fatality rate (CFR) of COVID-19 using the most updated COVID-19 epidemiological data before 13 September 2020. The dynamics in the CFR were analyzed using the Markov-switching autoregressive (MSAR) models. Results showed that the two-regime and three-regime MSAR approach better captured the non-linear dynamics in the CFR time series data for each of the top heavily infected countries including the world. The results also showed that rises in CFRs are more volatile than drops. We believe that this information can be useful for the government to establish appropriate policies in a timely manner.