Complexity最新文献

Opinion Dynamics is an interdisciplinary area of research. Disciplines of Psychology and Sociology have proposed models of how individuals form opinions and how social interactions influence this process. Sociophysicists have interpreted the observed patterns in opinion formation in individuals as arising out of nonlinearity in the underlying process and helped shape the models. Agent-based modelling has offered an excellent platform to study the Opinion Dynamics of large groups of interacting individuals. In this paper, we take recent models in opinion formation in individuals. We recast them to create a proper dynamical system and inject the idea of clock time into evolving individuals’ opinions. Thus, the time interval between two successive receipts of new information (i.e., the frequency of information receipts) by an individual becomes a factor that can be studied. In recent decades, social media has continuously shrunk time intervals between receipt of new information (i.e., increased frequency of information receipts). The recast models are used to show that as the time interval between successive receipts of new information gets shorter and the number of individuals in one’s network becomes larger, the propensity for polarization of an individual increases. This explains how social media could have caused polarisation. We use the word “polarisation” to mean an individual’s inability to hold a neutral opinion. A polarisation number based on sociological parameters is proposed. Critical values of the polarisation number beyond which an individual is prone to polarization are identified. These critical values depend on psychological parameters. The reduced time intervals between the receipt of new information and an increase in the size of groups that interact can push the polarisation number to approach and cross the critical value and could have played a crucial role in polarising individuals and social groups. We also define the extent of polarisation as the width of the region around neutral within which an individual is unable to have an opinion. Reported results are for values of model parameters found in the literature. Our findings offer an opportunity to adjust model parameters to align with empirical evidence. The models of opinion formation in individuals and the understanding arrived at in this study will help study Opinion Dynamics with all its nuances and details on large social networks using agent-based​ modelling.

The delayed intervention techniques in real-world problem modelling have a significant role in behavioural, social, physical, and biological engineering, biomathematical sciences, and many more disciplines. Delayed modelling of real-world problems is a powerful tool and nonpharmaceutical technique for understanding the dynamics of disease in a population. This paper considers real-world problems like the Lassa fever model. According to the World Health Organization (WHO), Benin, Ghana, Guinea, Liberia, Mali, Sierra Leone, Togo, Nigeria, and West Africa are the most affected countries with Lassa fever. The most dangerous situation is that eighty percent of the infected persons have no symptoms. To study the dynamics of Lassa fever, two types of populations are considered humans and rats. The human population includes susceptible, infected, and recovered. The rat population includes susceptible and infectious rodents. By introducing a delay parameter and decay exponential term into the existing model in the literature, we got the system of highly nonlinear delay differential equations (DDEs). The fundamental properties such as positivity, boundedness, existence, and uniqueness are verified for the said model. The equilibrium and reproduction number of the model are discussed. The reproduction number for the Lassa fever model is analyzed using the next-generation matrix method. If the reproduction number is less than one, this situation helps eradicate the disease. If the reproduction number is more significant than one, then the virus will spread rapidly in human beings. We have also investigated the effect of the delay factor on reproduction numbers. The local and global stabilities for both equilibria of the model have also been presented. Furthermore, computer simulations are designed to analyze the academic behaviour of the model.

We consider a deterministic optimal control approach with cost-effectiveness analysis for the diphtheria outbreak in the Rohingya refugee camp in Bangladesh. A deterministic epidemic dynamical model for diphtheria outbreaks has been developed with three optimal controls: vaccination, latent, and infectious treatment. Here, the qualitative study of the model has been interpreted. An objective function has been regarded as a cost function introduced by the optimal controls and the diseases themselves. Then, the existence and uniqueness of the optimal system have also been shown with the help of Pontryagin’s minimum principle. A numerical investigation has been carried out to solve the state and adjoint systems of optimality conditions. Furthermore, it has been investigated using several levels of availability of the optimal controls (vaccination, latent, and infectious treatment) to identify which level gives the best outcomes. Moreover, the cost-effective analysis has been inquired with the numerical value of the cost function and the total cured population in each control strategy to clarify the strategy with the least cost but maximum remediation.

We find that in the upstream status of global value chain, country effects are relatively stronger than industry effects; industry effects dominate country effects downstream of the global value chain. During financial crisis, downstream in the value chain, the influence of industry effects waned and country effects rose. Moreover, for developed countries, the negative impact of the upstream status of value chain weakened considerably; the impact of upstream status strengthened for emerging markets after the subprime mortgage crisis. For tradable industries, the negative impact of global value chain upstream status on pure industry-specific returns strengthens significantly.

We consider a continuous-time model describing the interaction between phytoplankton and zooplankton using a Holling type-II response. We then transform this continuous-time model into a discrete-time counterpart using a fractional-order discretization method. The paper explores the local stability of this obtained system concerning all equilibrium points and establishes the global asymptotic stability of its positive fixed point. The study also demonstrates that, under specific mathematical conditions, the system undergoes a Neimark–Sacker bifurcation around its positive equilibrium point. To effectively manage this bifurcation, two modified hybrid control techniques are introduced. The paper concludes by presenting illustrative numerical examples that validate the theoretical findings and assess the effectiveness and feasibility of the newly proposed control strategies. In addition, a comparative analysis is conducted between the modified hybrid techniques and an existing hybrid approach.

The field of mathematical inequalities has exerted a profound influence across a multitude of scientific disciplines, making it a captivating and expansive domain ripe for research investigation. This article offers estimations for the Slater difference through the application of the concept of convexity. We present a diverse type of applications that stem from the main findings related to power means, Zipf–Mandelbrot entropy, and within the field of information theory. Our main tools for deriving estimates for the Slater difference involve the triangular inequality, the definition of the convex function, and the well-established Jensen inequality.

Currently, soft robots alone cannot obtain the same operating speed as rigid robots, while rigid robots are not safe enough for human-robot interaction. To address this problem, this paper describes a hybrid robot system that combines both rigid and flexible systems for unknown domain exploration. The system consists of a four-wheeled robot chassis and a cylindrical pneumatic soft actuator, and finally, a computer is used to coordinate and control both. The hardware of the robot system is designed, a bending motion model is proposed, and SOFA framework is used to carry out finite element simulation (FEM) to verify the reasonableness of the design; linear motion speeds of up to 0.5 m/s, higher than the existing soft robots investigated, were verified experimentally separately after carrying the new module, and steering ability was retained; and the robot carrying the navigation module is verified to have a certain map building and localization function through the construction of the simultaneous localization and mapping (SLAM) experimental platform. The hybrid robot introduced in this paper can move quickly on flat terrain and can use its soft part to avoid wear and tear.

The uncertainty of parameters will have a significant impact on slope stability, where sensitivity analysis is a commonly used method in uncertainty research. However, traditional sensitivity analysis method costs much computation time. When calculating the sensitivity index of one parameter, all other parameters are taken as fixed values, and the uncertainty of all parameters cannot be considered simultaneously. Therefore, the variance-based and the moment-independent global sensitivity analysis (GSA) methods are both introduced to determine the influence of geotechnical parameters on slope stability in this study. To solve the importance index of GSA, the least angle regression algorithm, the kernel density estimation, and orthogonal polynomial estimation methods are developed to obtain variance-based importance index and the moment-independent importance index, respectively. The proposed methods allow all variables to change simultaneously within their variation range and have high computational efficiency. The results are in good at with those obtained by the variance-based Monte Carlo simulation method, which is considered as the exact solution forobtaining the importance index. The influence of the correlation between the shear strength parameters (c and φ) on the importance index is also studied, which indicates that the negative correlation will have a great impact on the importance index, which in turn affects the safety assessment of slope. Three engineering cases have been studied for engineering application, and the compared results indicate that the impact of the geotechnical parameters uncertainty on the safety factor (Fs) and failure probability (p_f) are different. Therefore, the approaches based on GSA which can integrate the Fs with p_f will be a promising approach for slope stability evaluation.

Systems are designed to perform specific task by giving certain input which produces the required output in an orderly manner known as process. The input, output, and the state variables should be known that will help in interacting with the system. The relation between these variables can be brought out by building a model that resembles or expresses the original performance of the system. The parameters of the model are estimated using the least squares approximation, maximum likelihood, maximum log-likelihood, and Bayesian parameter estimation methods by utilizing the experimental data from the multiprocess station. The selected parameters are converted to nine different transfer function models that represent the given dynamic system. The models framed are analyzed by the criterion curve technique using seven criterion functions evaluating the fitness of the model. Order of the model is found from Hankel matrix representation methods such as singular value decomposition and determinant method. Response of the models is compared with the original response to choose the best fit model by calculating ISE standard. All the above methods are used to model the system without physical and theoretical laws which is known as system identification.

In this article, we explore the utilization of the Caputo derivative and the Riemann–Liouville (R–L) fractional integral to analyze the optimal auxiliary function method for approximating fractional nonlinear long waves. Approximate long wave equation with a distinct dispersion relation offers the most accurate description of shallow water wave properties. Various methods, including the Adomian decomposition technique, the variational iteration method, the optimum homotopy asymptotic method, and the new iterative technique, have been employed and compared to those obtained using the fractional-order approximate long wave equation. The results of our study indicate that the optimal auxiliary function method is highly successful and practically simple, achieving better and more rapid convergence after just one repetition. This method is recognized as an efficient approach, demonstrating high precision in solving intriguing and intricate problems. Furthermore, it proves to be more time and resource efficient than other relevant analytical techniques, leading to significant savings in both volume and time. Compared to the Adomian decomposition technique, the new iterative technique, the variational iteration method, and the optimum homotopy asymptotic method, the suggested technique is extremely accurate computationally. It is also easy to analyze and solve fractionally linked nonlinear complex phenomena that arise in science and technology. We present the numerical and graphical findings that support these conclusions.