Communications in Nonlinear Science and Numerical Simulation最新文献

The difference between the computational peridynamic results and the corresponding exact classical solutions is contributed by the error induced by numerical discretization and the nonlocality-induced difference. To evaluate and compare these contributions and investigate their dependence on the peridynamic influence functions, in this paper, we apply different peridynamic influence functions and different horizon factors (m, the ratio between the horizon size and the grid spacing) to conduct static (or quasi-static) tensile numerical tests. We calculate the difference between the peridynamic solutions and the corresponding classical solutions for static uniaxial tension of thin plates with or without hole, the J-integral of a single crack under Mode I loading condition, and the quasi-static fracture in a perforated thin plate. For the case of uniaxial tension in a thin, homogeneous plate, we separate the effects of nonlocality and numerical discretization by implementing the boundary conditions in different ways. The numerical results show that both the effects of nonlocality and numerical discretization correspond to the nonlocal constants of the influence functions (with few exceptions). For problems with the presence of the peridynamic surface effect, such as holes, influence function with weaker nonlocality is a better choice to obtain more accurate results.

In this paper we study a nonlinear infection viral propagation model with diffusion, in which, the left boundary is fixed and with homogeneous Dirichlet boundary conditions, while the right boundary is free. We find that the habitat always expands to the half line $[0,\infty )$, and that the virus and infected cells always die out when the Basic Reproduction Number $R_0\le 1$, while the virus and infected cells have persistence properties when $R_0>1$. To obtain the persistence properties of virus and infected cells when $R_0>1$, the most work of this paper focuses on the existence and uniqueness of bounded positive equilibrium solutions for subsystems and the existence of positive equilibrium solutions for the entire system.

In this paper, we probe the $p$th moment exponential stability ($p-$ES) of stochastic delayed systems subject to event-triggered delayed impulsive control (ETDIC), where the impulsive intensities are assumed to be positive random variables. Based on event-triggered mechanism (ETM) in the sense of expectation, some new sufficient conditions are developed to ensure the stability of the addressed system with Zeno-free behavior. The Lyapunov–Razumikhin method is adopted to handle the time-varying delay in continuous dynamics, and the concept of average random impulsive estimation (ARIE) is introduced to reduce the design requirements of the controller. Especially, the proposed ETDIC strategy not only generates the impulse time sequence according to the predesigned ETM, but also removes the limitations on the size of time delays. Furthermore, the ETM serves as a solution for synchronization problems in complex neural networks. Finally, two examples are given to illustrate the effectiveness of our conclusions.

In the Graph-let based time series analysis, a time series is mapped into a series of graph-lets, representing the local states respectively. The bridges between successive graph-lets are reduced simply to a linkage with an information of occurrence. In the present work, we focus our attention on the bridge series, i.e., preserve the structures of the bridges and reduce the states into nodes. The bridge series can tell us how the system evolves. Technically, the ordinal partition algorithm is adopted to construct the graph-lets and the bridges. Results for the Logistic Map, the Hénon Map, and the Lorenz System show that the statistical properties for transition frequency network for the bridges, e.g., the number of visited bridges and the average out-entropy-degree, have the capability of characterizing chaotic processes, being equivalent with the Lyapunov exponent. What is more, the topological structure can display the details of the contributions of the transitions between the bridges to the statistical properties.

This paper considers the inhomogeneous biaxial nematic liquid crystal flow in a smooth bounded domain $\Omega \subset R^2$, where the velocity $u$ and the orthogonal unit vector fields $(m,n)$ admit the Dirichlet and Neumann boundary condition, respectively. By applying piecewise estimate and continuity method, we get the global existence of strong solutions, provided that the basic energy is suitably small. Our result may be regarded as an extension and improvement of Gong-Lin (2022) and Li-Liu-Zhong (2017) to the Neumann boundary condition, where the initial vacuum is allowed. Some new techniques are developed in order to deal with integral estimates caused by the boundary condition, and more complicated model.

The dynamic model for perturbative longitudinal vibration of microresonators subjected to the parallel-plate electrostatic force, which can be converted into a cubic oscillator with nonlinear polynomials, is established in this manuscript. The orbits and global dynamical behaviors of the cubic oscillator at full state are studied both analytically and numerically. The expressions of homoclinic orbits and subharmonic orbits are obtained analytically by solving the Hamilton system. The scenarios of phase portraits and equilibria are given. With the Melnikov method, the critical value of chaos arising from homoclinic intersections is derived analytically. The investigation yields intriguing dynamical phenomena, including the controllable frequencies that regulate the system without inducing chaos. The conditions for the occurrence of subharmonic bifurcations of integer order are presented with the subharmonic Melnikov method. Besides, the results indicate that the system does not undergo fractional order subharmonic bifurcation and it can reach a chaotic state through a finite number of integer order subharmonic bifurcations. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré cross-sections, Lyapunov exponential spectrums and basins of attractor are given, which are consistent with theoretical results.

The research on stability analysis and control design for random nonlinear systems have been greatly popularized in recent ten years, but almost no literature focuses on the fractional-order case. This paper explores the stability problem for a class of random Caputo fractional-order nonlinear systems. As a prerequisite, under the globally and the locally Lipschitz conditions, it is shown that such systems have a global unique solution with the aid of the generalized Gronwall inequality and a Picard iterative technique. By resorting to Laplace transformation and Lyapunov stability theory, some feasible conditions are established such that the considered fractional-order nonlinear systems are respectively Mittag-Leffler noise-to-state stable, Mittag-Leffler globally asymptotically stable. Then, a tracking control strategy is established for a class of random Caputo fractional-order strict-feedback systems. The feasibility analysis is addressed according to the established stability criteria. Finally, a power system and a mass–spring-damper system modeled by the random fractional-order method are employed to demonstrate the efficiency of the established analysis approach. More critically, the deficiency in the existing literatures is covered up by the current work and a set of new theories and methods in studying random Caputo fractional-order nonlinear systems is built up.

Optimization techniques play a pivotal role in refining problem-solving methods across various domains. These methods have demonstrated their efficacy in addressing real-world complexities. Continuous efforts are made to create and enhance techniques in the realm of research. This paper introduces a novel technique that distinguishes itself through its clarity, logical mathematical structure, and robust mathematical equations, particularly in the second phase. This study presents the development of a new metaheuristic algorithm named Coyote and Badger Optimization (CBO). CBO draws inspiration from the cooperative behaviors observed in honey badgers and coyotes, with a specific focus on their intriguing communication process. Utilizing the inherent traits of these animals, the proposed CBO algorithm offers an intuitive and effective solution for addressing engineering optimization challenges by providing the best fitness values. To validate CBO's effectiveness in real-time applications, complex engineering problems called pressure vessel design, feature selection in medical system, and tension-compression spring design are used as case studies for testing the proposed CBO compared to other recent algorithms. Additionally, ten benchmark functions and also statistical analysis methods (mean, standard deviation, confidence intervals, t-test, and Wilcoxon test) are used. Experimental results demonstrate that the CBO algorithm surpasses eleven recent algorithms when subjected to common ten benchmark functions. Additionally, CBO outperforms other recent eleven algorithms according to three different case studies. According to the ten benchmark functions (F1 to F10), CBO provides the minimum fitness values which are closed to the exact (standard) values; 0, 0, 0.003, 0.0002, -1.0316, 3.0058, 0.398, 0.02, 0.00076, and 0.000725 respectively. Related to statistical analysis, CBO provides the best mean, standard deviation, confidence intervals, t-test, and Wilcoxon test values. According to case studies, CBO provided the minimum cost value for pressure vessel design, the maximum accuracy value for feature selection, and the minimum cost value for spring design. Hence, CBO superiors other recent algorithms.

In this paper, a stochastic tumor–immune model with comprehensive pulsed therapy is established by taking stochastic perturbation and pulsed effect into account. Some properties of the model solutions are given in the form of the Theorems. Firstly, we obtain the equivalent solutions of the tumor–immune system by through three auxiliary equations, and prove the system solutions are existent, positive and unique. Secondly, a Lyapunov function is constructed to prove the global attraction in the mean sense for the system solution, and the boundness of the solutions’ expectation is proved by the comparison theorem of the impulsive differential equations. Next, the sufficient conditions for the extinction and non-mean persistence of tumor cells, hunting T-cells and helper T-cells, as well as the weak persistence and stochastic persistence of the tumor, are obtained by way of combining It$\hat{o}$’s differential rule and strong law of large numbers, respectively. The results pass the confirmation by numerical Milsteins method. The results show that when the noise intensity gradually increases, the tumor state changes from the weak persistence to the extinction, it demonstrates that the effect of stochastic perturbations on tumor cells is very prominent. In addition, by adjusting the value of $a\left(nP\right)$ to simulate different medication doses, the results show that the killing rate of the medication to the tumor cells is the dominant factor in the long-term evolution of the tumor, and the bigger killing rate can lead to a rapid decrease in the number of tumor cells. Increasing the frequency of pulse therapy has also significant effects on tumor regression. The conclusion is consistent with the clinical observation of tumor treatment.

This paper is mainly concerned with introducing a numerical method for solving initial–boundary value problems with integer and fractional order time derivatives. The method is based on discretizing the considered problems with respect to spatial and temporal domains. With the help of finite difference methods, we transformed the studied problem into a set of fractional differential equations. Then, we implemented the fractional Adams method to solve this set in order to provide approximate solutions to the main problem. This combination results in an algorithm that can efficiently and accurately solve a general class of integer and fractional order initial–boundary value problems, such that it does not need to solve large systems of linear equations. In addition, we discussed the stability of the proposed scheme. Three illustrative examples are numerically solved to reveal the effectiveness and validity of the proposed technique.