Mathematical Problems in Engineering

In this study, we examine the dynamics of a discrete-time predator–prey system with prey refuge. We discuss the stability prerequisite for effective fixed points. The existence criteria for period-doubling (PD) bifurcation and Neimark–Sacker (N–S) bifurcation are derived from the center manifold theorem and bifurcation theory. Examples of numerical simulations that demonstrate the validity of theoretical analysis, as well as complex dynamical behaviors and biological processes, include bifurcation diagrams, maximal Lyapunov exponents, fractal dimensions (FDs), and phase portraits, respectively. From a biological perspective, this suggests that the system can be stabilized into a locally stable coexistence by the tiny integral step size. However, the system might become unstable because of the large integral step size, resulting in richer and more complex dynamics. It has been discovered that the parameter values have a substantial impact on the dynamic behavior of the discrete prey–predator model. Finally, to control the chaotic trajectories that arise in the system, we employ a feedback control technique.

This paper presents a control strategy for a photovoltaic (PV)-based distributed generator (DG) to enhance the frequency regulation of a microgrid. A microgrid is a small-scale power system that integrates distributed energy sources and interconnected loads, which can operate independently or in parallel with the main grid. However, the high integration of DGs poses stability problems, particularly the frequency regulation under contingencies in the microgrid. For example, the shutdown of one generating unit or the reduction of system inertia owing to the high integration of converter-based DGs will increase the risk of instability of the microgrid and the main grid. Therefore, maintaining and increasing the frequency regulation capability is crucial in microgrid operation. This paper focuses on developing a controller for PV DG based on virtual inertia control combined with the conventional control method of a converter in order to regulate the microgrid frequency under contingency. The proposed control strategy for a PV-based DG is then verified through simulation of the 14-bus microgrid model using MATLAB/Simulink, showing regulation in frequency under island mode operation of the microgrid. In addition, comparisons between the original and proposed control strategy microgrid model are then carried out.

Different solid materials are widely used in various constructions due to their availability and low cost. However, cracks or conversions in the structures can affect their stiffness and vibration signatures. This research aims to evaluate the load distribution, deformation, and the effects of the cracks on the natural frequencies and deformations of iron, steel, and titanium beams. A finite element-based model and COMSOL Multiphysics software were employed to measure and compare the frequencies and strengths of the beams. The results showed that the frequencies increased with the load, and titanium beams had the highest frequencies and deflections, while steel beams had the highest stress resistance. This frequency analysis can help to detect very small cracks (less than 0.05 mm) in the beams. The study concluded that steel is the most suitable material for construction due to its elasticity, availability, and low cost.

In this manuscript, the primary motivation is the implementation of the advanced -expansion method to construct the soliton solution, which contains some controlling parameters of two distinct equations via the Biswas–Arshed model and the (3 + 1)-dimensional Kadomtsev–Petviashvili equation. Here, the solutions’ behaviors are presented graphically under some conditions on those parameters. The height of the wave, wave direction, and angle of the obtained wave is formed by substituting the particular values of the considerations over showing figures with the control plot. With the collaboration of the advanced -expansion method, we construct entirely the solitary wave results as well as rogue type soliton, combined singular soliton, kink, singular kink, bright and dark soliton, periodic shape, double periodic shape soliton, etc. Therefore, it is remarkable to perceive that the advanced -expansion technique is a simple, viable, and numerical solid apparatus for clarifying careful outcomes to the other nonstraight equivalences.

The problems of operating range and costs are the two most critical bottlenecks restricting the extensive application of electric vehicles (EVs) in China and some other countries. There are also some prominent problems in China’s EVs, which lead to poor competitiveness of EVs compared with traditional internal combustion engine vehicles. This paper analyzes the key mathematical factors restricting the development and popularization of EVs in China from the aspects of strategic policy, sales situation, and self-problems. For the best-selling family cars in China, select the representative models with the same body structure, and make statistics on various parameters most concerned by consumers, establish a database through data statistics and analysis software. Through summarizing France’s standardization development strategy and relevant issues reflected by the development data of its EVs, this paper puts forward the hypothesis leading the development of EVs through standardization to enhance their competitiveness, gives the specific suggestions, and briefly analyzes the feasibility from the aspects of product situation. The research content of this paper provides a certain basis and ideas for the future research work.

The formation mechanism of the resultant electric field is complex under parallel operation of extra-high-voltage alternating current (AC)/direct current (DC) transmission lines. However, existing methods are computationally expensive and fail to guarantee the stability and convergency of results. To solve this problem, a calculation method with nonuniform grids and varying time steps was proposed on the basis of the finite-volume and finite-element method for calculating the ground resultant electric field of parallel AC/DC transmission lines. The selection of the initial value of space charges and the setting of the surface charge density of conductors were also improved, which greatly enhanced the computational stability and efficiency. Then, the improved method was adopted to calculate the ground resultant electric field under parallel operation of a 750-kV AC transmission line and a ±800-kV DC transmission line when considering and not considering wind deviation. Results show that, when ignoring wind deviation, the normalized values of the ground resultant electric field within 6 m from the side-phase conductor of the AC line are always less than 1 under conditions of the minimum clearances to earth of the AC and DC lines passing through a residential area stipulated in the national standards, which meets codified requirements. When considering wind deviation, instead of an increase, the calculated ground resultant electric field of parallel AC/DC lines is significantly reduced, and the weighted value is much less than the limiting value.