Chaos, Solitons and Fractals: X最新文献

At present, the solution and qualitative analysis of nonlinear partial differential equations occupy a very important position in the study of dynamics. In this paper, the bilinear Bäcklund transformation of the (2+1)-dimensional variable-coefficient $Gardner-KP\left(GKP\right)$ equation is deduced by virtue of Hirota bilinear form, which consists of seven bilinear equations and involves ten arbitrary parameters. On the basis of the bilinear Bäcklund transformation, the traveling wave solution of the equation is obtained. Then the test function of the interaction solution of the positive quadratic function and exponential function of the (2+1)-dimensional variable-coefficient $GKP$ equation is constructed, and then the test function of the positive quadratic function, hyperbolic cosine function and the interaction solution of the cosine function is constructed. With the help of mathematical symbol software Maple and Mathematica, the solitary wave solutions of (2+1)-dimensional variable-coefficient $GKP$ equation is obtained by using Maple and Mathematica, and the interaction phenomena between a Lump wave and a Kink wave, a Lump wave and Multi-Kink waves are discussed.

Fungicides are consumed to foreclose or slow the epidemics of disease germ by fungi. Crop cultivation is a favorable business platform for farmers, but it is also very common for them to have losses. These losses happen by attacking pathogens, such as fungi, oomycetes (water fungi), viruses, bacteria, nematodes, and viroid that spread the infection into the plants. In this article, we derive a fractional mathematical model for simulating the dynamics of fungicide application via Caputo-Fabrizio fractional derivative. Caputo-Fabrizio operator is defined with non-singular type kernel which is better than singular kernel. We give some important proofs related to the existence of a unique solution of the given model. We derive the solution of the model by using the Adams-Bashforth algorithm and also mentioned the stability of the method. We plotted the number of graphs at different fungicide application rate, fungicide decay rate, fungicide effectiveness, curatives rate of fungicide, growth rate of the host, and removal rate. A complete structure of the given problem can be understood by this paper. The main novelty of this work is to understand the role of fungicide application in the disease caused by fungi with the help of fractional derivatives consisting memory effects.

In this research article the residual power series method is implemented for the solution of the Navier-stokes equations with two and three dimensions having the initial conditions. Caputo operator is used for the fractional derivative. The formulation is made in general form and then applied to the specific problems to check the validity of the suggested method. The solution of some numerical examples of the Navier-stokes equations are presented for both fractional and integer orders of the problems. The comparison of the obtained and exact solution is provided by using 2D and 3D plots of the solutions which confirmed the higher accuracy of the proposed method. Tables are drawn to show the results obtained, exact solutions and absolute error of the suggested method for each problem. It is investigated that as the number of terms increase in the series solution of the problems, the obtained solutions have the closed contact with actual solutions of each problem. From the calculated values it is cleared that the method is accurate and easy and therefore can be extended further to linear and nonlinear problems.

In this work, we develop a sophisticated mathematical model for dengue transmission dynamics based on vaccination, reinfection and carrier class assumptions. We utilize Caputo-Fabrizio fractional framework to represent the transmission phenomena of dengue. For the model analysis, the basic theory and findings of the Caputo-Fabrizio fractional operator are provided. We utilize the next-generation approach to calculate the threshold parameter $R_0$ for our proposed dengue infection model. We have shown that the disease-free steady-state of the hypothesized dengue system is locally asymptotically stable if $R_0<1$ and is unstable in other conditions. The reproduction number of the system of dengue infection is investigated numerically. Furthermore, under the Caputo-Fabrizio approach, we offer a numerical approach for solving our fractional-order problem. We obtain the solution pathways of our system with various values of fractional-order $\vartheta$ and other input values in order to illustrate the effects of fractional-order $\vartheta$ and other input values on our system. Based on our findings, we forecast the most essential system factors for eradicating dengue infections.

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.