The dynamical behaviour of traveling waves in a class of two-dimensional system whose amplitude obeys the two-dimensional complex cubic-quintic Ginzburg-Landau equation is deeply studied as a function of parameters near a subcritical bifurcation. Then, the bifurcation method is used to predict the nature of solutions of the considered wave equation. It is applied to reduce the two-dimensional complex cubic-quintic Ginzburg-Landau equation to the quintic nonlinear ordinary differential equation, easily solvable. Under some constraints of parameters, equilibrium points are obtained and phase portraits have been plotted. The particularity of these phase portraits obtained for new ordinary differential equation is the existence of homoclinic or heteroclinic orbits depending on the nature of equilibrium points. For some parameters, one has the orbits starting to one fixed point and passing through another fixed point before returning to the same fixed point, predicting then the existence of the combination of a pair of pulse-dark soliton. One has also for other parameters, the orbits linking three equilibrium points predicting the existence of a dark soliton pair. These results are very important and can predict the same solutions in many domains, particularly in wave phenomena, mechanical systems, or laterally heated fluid layers. Moreover, depending on the values of parameter systems, the analytical expression of the solutions predicted is found. The three-dimensional graphs of these solutions are plotted as well as their 2D plots in the propagation direction.

This paper investigates the dynamics of systemic risk in banking networks by analyzing equilibrium points and stability conditions. The focus is on a model that incorporates interactions among distressed and undistressed banks. The equilibrium points are determined by solving a reduced system of equations, considering both homogeneous and heterogeneous scenarios. Local and global stability analyses reveal conditions under which equilibrium points are stable or unstable. Numerical simulations further illustrate the dynamics of systemic risk, while the theoretical findings offer insights into the behavior of distressed banks under varying conditions. Overall, the model enhances our understanding of systemic financial risk and offers valuable insights for risk management and policymaking in the banking sector.

Robot-assisted intramedullary nailing is a minimally invasive surgical procedure commonly used to treat femur fractures. Despite its benefits, there are several disadvantages associated with this technique, such as frequent malalignment, physical fatigue, and excessive radiation exposure for medical personnel. Therefore, it is crucial to ensure that robotic surgery for fracture reduction is precise and safe. Precise calculation and regulation of the robot’s reduction force are of utmost importance. In this study, we propose a manipulator that utilises robot assistance and indirect contact with the femur to effectively reduce fractures in the shaft. The dynamics of the reduction robot are analysed using the implicit function theorem, which allows us to address the reduced problem. A parametric approach is presented to tackle the initial algebraic constraints, enabling the approximation of the state-space solution while simultaneously controlling the class of constraints in a multiway manner. This approach simplifies the problem from an infinite-dimensional one to a finite-dimensional one, leading to an approximate solution obtained by solving a set of control linear algebraic equations. The proposed robotic-assisted system enhances fracture repositioning while reducing radiation exposure for both the patient and the medical staff. Through numerical results and their practical application, we have developed an efficient method that yields positive outcomes.

Coffee berry disease (CBD) is a fungal disease caused by Colletotrichum kahawae. CBD is a major constraint to coffee production to Kenya and Africa at large. In this research paper, we formulate a mathematical model of the dynamics of the coffee berry disease. The model consists of coffee plant population in a plantation and Colletotrichum kahawae pathogen population. We derived the basic reproduction number R k 0 , and analyzed the dynamical behaviors of both disease-free equilibrium and endemic equilibrium by the theory of ordinary differential equations. Using the MATLAB ode45 solver, we carried out numerical simulation, and the findings are consistent with the theoretical results.

With the continuous development of information technology and the continuous progress of traffic bandwidth, the types and methods of network attacks have become more complex, posing a great threat to the large-scale campus network environment. To solve this problem, a network traffic anomaly detection model based on subspace information entropy flow matrix and a subspace anomaly weight clustering network traffic anomaly detection model combined with density anomaly weight and clustering ideas are proposed. Under the two test sets of public dataset and collected campus network data information of a university, the detection performance of the proposed anomaly detection method is compared with other anomaly detection algorithm models. The results show that the proposed detection model is superior to other models in speed and accuracy under the open dataset. And the two traffic anomaly detection models proposed in the study can well complete the task of network traffic anomaly detection under the large-scale campus network environment.

In the present article, the time fractional Fisher equation is considered in conformal form to study the application of the Lie classical method and quantitative analysis. The Lie symmetry method has been applied to find the infinitesimal generators and symmetry reductions of the fractional Fisher equation. The obtained reduced form of the equation is solved by the method of G ′ / G , which gives different forms of solutions. The theory of bifurcation has been utilized in the reduced form to check the stability and nature of critical points by transforming the equations into an autonomous system. Some phase portraits have been drawn at different critical points by the use of maple.

The purpose of this paper is to investigate the valuation of equity-linked death benefit contracts and the multiple life insurance on two heads based on a joint survival model. Using the exponential Wiener process assumption for the stock price process and a K n distribution for the time until death, we provide explicit formulas for the expectation of the discounted payment of the guaranteed minimum death benefit products, and we derive closed expressions for some options and numerical illustrations. We investigate multiple life insurance based on a joint survival using the bivariate Sarmanov distribution with K n (i.e., the Laplace transform of their density function is a ratio of two polynomials of degree at most) marginal distributions. We present analytical results of the joint-life status.

The novel coronavirus is a recently discovered member of one of the largest families of viruses with symptoms ranging from a simple cold to excruciating respiratory agony. In the present paper, a deterministic mathematical model is formulated to estimate the transmission dynamics of COVID-19 with the inclusion of control strategies like (i) double-dose vaccination, (ii) prevention, and (iii) treatment. In addition, instead of considering all infectious humans as one unit, we separate them into symptomatic and asymptomatic groups, and the impact is analyzed. This separation is meaningful because various reports indicate that the asymptomatic cases will spread the disease more than the symptomatic cases. The model is proved to be mathematically well-posed and biologically meaningful by showing positivity and boundedness of the solution using the appropriate initial conditions. For the reproduction number, a parametric formula is constructed, and also the associated numerical value is calculated from the reported real data in Ethiopia. Moreover, disease-free and endemic equilibria are determined, and their local and global stabilities are discussed using the Lyapunov function technique. These equilibria are found to be locally asymptotically stable if R 0 < 1 and R 0 > 1 , respectively. Following the model fitting and estimation of the parameter values, sensitivity analysis was performed in order to analyze the impact of each parameter on transmission dynamics. In other words, this study can be used to evaluate how major model parameters affect transmission dynamics and control. Utilizing Pontryagin’s maximal principle, the best control measures are implemented with the aim of lowering the burdens associated with infection, prevention, and treatment. To comprehend and visualize the impact of control techniques on the development of the disease and to illustrate the analytical findings generated in this study, numerical simulation studies are conducted. Finally, the output of the study illustrates that adhering to all the control strategies has a big impact on minimizing the transmission of the disease in society. Which means that if the control strategies are well managed by the concerned body, then the burden of the disease is reduced quickly in the Ethiopian population.

In the two-sided market where the third-party platforms connect the providers and consumers, the online platforms become the significant distribution channel of digital products; therefore, the digital product firms face the hybrid channel pricing problem in the two-sided market in which the products are launched through the platform channel and the existing direct channel. Because the network externality effect is the significant economic characteristic of digital products and services, the current work presents the models of consumers’ utility obtained by adopting digital products from the direct and platform channels, and the utility models use the network effect in the direct and platform channels as the parameters. The optimization model on pricing is derived from the utility models and solved mathematically. The closed-form solutions show that the price in the direct channel is supposed to be lower than that in the platform channel, while the prices of digital products would be affected by the network effect only when the products are distributed through the direct channel. The comparative statics analysis on the network effect illustrates that the network effect in the direct channel and the platform channel would, respectively, have the positive and negative impact on the products’ prices and the firms’ profit. The current work explores the hybrid channel pricing problem and provides insights for the digital product firms on the optimal pricing decision in the context of the emerging platform economy.

In this paper, we introduce a new generalized inverse, called the G-MPCEP inverse of a complex matrix. We investigate some characterizations, representations, and properties of this new inverse. Cramer’s rule for the solution of a singular equation A x = B is also presented. Moreover, the determinantal representations for the G-MPCEP inverse are studied. Finally, the G-MPCEP inverse being used in solving appropriate systems of linear equations is established.