Discrete Dynamics in Nature and Society

In this article, a real case of a one MW PV substation design problem is described. The impact of the tolerances of power components (mainly inductors and capacitors) on the design is highlighted through two studies using two different control strategies that are selective harmonic elimination (SHE) and selective harmonic modulation (SHM). The obtained results show that the components’ tolerances have a significant effect on the design, especially for the SHE strategy. While the design using SHM control shows a weak sensitivity to the components’ tolerance. In this study, an upgrade of the most sensitive control strategy is proposed in order to improve its sensitivity against components’ tolerance. The results show that the strategy upgrading leads not only to improving the sensitivity but also to generating better power quality.

The complex dynamics of a nonlinear discretized predator-prey model with the nonlinear Allee effect in prey and both populations are investigated. First, the rigorous results are derived from the existence and stability of the fixed points of the model. Second, we establish a model with the Allee effect in prey undergoing codimension-one bifurcations (flip bifurcation and Neimark–Sacker bifurcation) and codimension-two bifurcation associated with 1 : 2 strong resonance by using center manifold theorem and bifurcation theory, and the direction of bifurcations is also evaluated. In particular, chaos in the sense of Marotto is proved at some certain conditions. Third, numerical simulations are performed to illustrate the effectiveness of the theoretical results and other complex dynamical behaviors, such as the period-3, 4, 6, 8, 9, 30, and 43 orbits, attracting invariant cycles, coexisting chaotic sets, and so forth. Of most interest is the finding of coexisting attractors and multistability. Moreover, a moderate Allee effect in predators can stabilize the dynamical behavior. Finally, the hybrid feedback control strategy is implemented to stabilize chaotic orbits existing in the model.

Artificial intelligence plays a decisive role in the healthy and sustainable development of society. The rapid development of the economy and society has put forward higher standards and requirements for fire supervision. The development of science and technology has advanced the intelligence on fire protection. Through the application of intelligent fire control, the fire department can better supervise the fire control of various units and further improve the pertinence and effectiveness of fire control supervision. Artificial intelligence technology is widely used in all stages of construction projects, which brings many conveniences to the construction and use of projects. Based on the analysis of the current situation and existing problems of the basic maintenance of fire-fighting facilities, this project analyzes the effect of the application of artificial intelligence technology in the management of fire-fighting facilities. Therefore, the purpose of this project is to study the role and effectiveness of artificial intelligence technology in the management of fire-fighting facilities and further verify this conclusion with questionnaires and interviews.

We examine whether and how interest rate liberalization affects firm leverage in China. We find that interest rate liberalization exerts a negative effect on the leverage of firms. Specifically, firms experience a reduction in total leverage during the liberalization period, and firms’ short-term leverage declines more relative to long-term leverage. Mechanism analysis shows that firms with high information asymmetry enjoy more decline in leverage relative to firms with low information asymmetry, and further, liberalization policy enables the reduction in credit transaction costs, which indicates that the behavior of banks actively collecting corporate information is an important channel that interest rate liberalization impacts firm leverage. Finally, in additional tests, we find that the impact is more salient when firms are non-state-owned, and loss making. Compare to operating liabilities, firms experience more reduction in financial liability.

Measles is one of the top communicable diseases, which is still responsible for 2.6 million deaths every year. Due to this reason, the paper focuses on measles transmission dynamics concerning the impact of indirect contact rate (transmitted from the host of the virus to the healthy individual) and improving the SEVIR model into the SVIRP model. From the model, we first estimated the disease-free equilibrium, calculated the effective reproduction number , and established the stability analysis. The Castillo–Chavez stability criterion is used to demonstrate the global stability of the disease-free equilibrium point, while the linearization method is used to justify its local stability analysis and gives a result . The stability analysis of endemic equilibrium point is explained by defining a Lyapunov function, and its global stability exists when . To identify the effect of parameters on the transmission dynamics, we performed sensitivity index and numerical simulation. From the result, we obtained that the indirect contact rate has the highest impact in maximizing the transmission dynamics of measles. Also, we found that working on prevention and treatment strategies brings a significant contribution in reducing the disease effect in the community.

In this article, the behaviour of tumour growth and its interaction with the immune system have been studied using a mathematical model in the form of partial differential equations. However, the development of tumours and how they interact with the immune system make up an extremely complex and little-understood system. A new mathematical model has been proposed to gain insight into the role of immune response in the tumour microenvironment when no treatment is applied. The resulting model is a set of partial differential equations made up of four variables: the population density of tumour cells, two different types of immune cells (CD4+ helper T cells and CD8+ cytotoxic T cells), and nutrition content. Such kinds of systems also occur frequently in science and engineering. The interaction of tumour and immune cells is exemplified by predator-prey models in ecology, in which tumour cells act as prey and immune cells act as predators. The tumour-immune cell interaction is expressed via Holling’s Type-III and Beddington-DeAngelis functional responses. The combination of finite volume and finite element method is used to approximate the system numerically because these approximations are more suitable for time-dependent systems having diffusion. Finally, numerical simulations show that the methods perform well and depict the behaviour of the model.