Complexity最新文献

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.