Mathematics and Computers in Simulation最新文献

Multimodal multi-objective optimization problems (MMOPs) represent a highly challenging class of complex problems, characterized by the presence of several Pareto solution sets in the decision space which map to the identical Pareto-optimal front. The goal of solving MMOPs is to find multiple distinct Pareto sets to sustain a balance between good convergence and diversification of populations. In this paper, a multi-objective sand cat swarm optimization algorithm (MOSCSO) is developed to address MMOPs. In the MOSCSO algorithm, an adaptive clustering-based specific congestion distance technique is introduced to compute the level of crowdedness. This ensures an even distribution of individuals, avoiding excessive crowding in the local area. Subsequently, enhanced search-and-attack prey updating mechanisms are designed to effectively increase not only the exploration and exploitation capabilities of the algorithm but also to enhance the diversity of the swarm in both the decision space and the objective space. To verify the effectiveness of the proposed algorithm, the MOSCSO is applied to solve the CEC2019 complex multimodal benchmark function. The experimental outcomes illustrate that the proposed approach possesses excellent performance in searching for Pareto solutions compared with other algorithms. Meanwhile, the method is also employed to address the map-based distance minimization problem, which further validates the usefulness of the MOSCSO.

The proposed approach differs from existing works in that it models the constraints of each follower as a nonlinear strict feedback system, rather than relying on a desired reference trajectory for accessible subsystems. To address the limitations caused by uncertain terms in systems, radial basis functions neural networks are utilized to compensate for these unknown nonlinear terms. This leads to a novel distributed adaptive consensus tracking control protocol for high-order nonlinear heterogeneous multi-agent systems, based on the backstepping technique. By introducing a non-zero parameter in the traditional radial basis functions neural network, a new universal approximation is constructed, which overcomes the limitation of the approximation’s finite domain. Additionally, the approximation precision can be adjusted online using provided laws, and the dimension explosion of virtual and real control gains can be avoided through the use of the designed control approach. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

We introduce a generalization of the 4 compartments SVIR epidemic model discussed in [1] for the first time. Our model has K+4 compartments. K-1 of these compartments represent additional subsequent vaccination stages not considered in the original SVIR model, while a further compartment accounts for dead people. We analyze the equilibrium points of the model. A time-varying parameters version of it, having $K=3$ vaccination compartments, is then calibrated to Italian COVID-19 dataset. This analysis is carried out for three specific sub-periods: the first one, ranging from February 24th, 2020, up to December 26th 2020, when no vaccines were available; the second one, from the December 27th, 2020 up to December 31st, 2021, during which the Delta variant of the virus prevailed and Delta-targeted vaccination doses were administered to the population for the first time; finally, the last considered period is ranging from January 10th, 2022 up to June 3rd, 2022, and it was characterized by the diffusion of the Omicron variant. To tackle the problem of undetected infected or undetected recovered people we adopt an approach relying on different scenarios. The calibration of the model uses the property that the discrete-time version of it turns out to be explicitly solvable with respect to the parameters, hence providing a daily estimate of the involved parameters. This produces meaningful evolution patterns of the COVID-19 epidemic which allow a better understanding of the diffusive behavior of the pandemic along time. Lastly a statistical analysis of the epidemiological parameters estimators supports the non stationarity of their time series.

We develop adaptive time-stepping strategies for Itô-type stochastic differential equations (SDEs) with jump perturbations. Our approach builds on adaptive strategies for SDEs.

Adaptive methods can ensure strong convergence of nonlinear SDEs with drift and diffusion coefficients that violate global Lipschitz bounds by adjusting the stepsize dynamically on each trajectory to prevent spurious growth that can lead to loss of convergence if it occurs with sufficiently high probability.

In this article, we demonstrate the use of a jump-adapted mesh that incorporates jump times into the adaptive time-stepping strategy. We prove that any adaptive scheme satisfying a particular mean-square consistency bound for a nonlinear SDE in the non-jump case may be extended to a strongly convergent scheme in the Poisson jump case, where the jump and diffusion perturbations are mutually independent, and the jump coefficient satisfies a global Lipschitz condition.

In this paper, we have proposed and analyzed a predator–prey system introducing the cost of predation fear into the prey reproduction with Holling type-II functional response in the stochastic environment with the consideration of non-linear harvesting on predators. The system experiences Transcritical, Saddle–node, Hopf, and Bogdanov-Taken (BT) bifurcation with respect to the intrinsic growth rate and competition rate of the prey populations. We have discussed the existence and uniqueness of positive global solution of the stochastic model with the help of Ito’s integral formula and the long-term behavior of the solution is derived here. The existence of stationary distribution and explicit form of the density function is established here when only prey populations survive or both populations. We have shown that due to high fluctuation, the regime changes from one stable state to another state when bistability occurs in the system. The paper ends with some conclusions.

It is generally known that the error function is one of the key factors that determine the convergence, stability and generalization ability of neural networks. For most feedforward neural networks, the squared error function is usually chosen as the error function to train the network. However, networks based on the squared error function can lead to slow convergence and easily fall into local optimum in the actual training process. Recent studies have found that, compared to the squared error function, the gradient method based on the entropy error function measures the difference between the probability distribution of the model output and the probability distribution of the true labels during the iterative process, which can be more able to handle the uncertainty in the classification problem, less likely to fall into a local optimum and can learn to converge more rapidly. In this paper, we propose a batch gradient method for Sigma-Pi-Sigma neural networks based on the entropy error function and rigorously demonstrate the weak and strong convergence of the new algorithm in the batch input mode. Finally, the theoretical results and effectiveness of the algorithm are verified by simulation.

This article establishes a bifurcation analysis of a singularly perturbed piecewise-smooth continuous predator–prey system with a sufficiently small parameter. The bifurcation that can generate limit cycles here is our main concern. To achieve this goal, we have developed a lemma that is used to determine the parameter region that can generate limit cycles. Further conclusions indicate that the existence of a 2-shaped critical manifold is required. Based on the Poincaré-Bendixon lemma, Fenichel’s theory and geometric singular perturbation theory, we demonstrate the possibility of generating smooth and nonsmooth bifurcations. In fact, nonsmooth bifurcations only occur in piecewise-smooth systems. More specifically, different types of nonsmooth bifurcations are also presented in this article, including nonsmooth Hopf bifurcation, Hopf-like bifurcation and super-explosion. In addition, this article discusses the existence of crossing limit cycles and explains whether the crossing limit cycle is characterized by canard cycles without head, canard cycles with head or relaxation oscillations. Furthermore, the coexistence of two relaxation oscillations, the coexistence of two canard cycles without head, and the coexistence of one relaxation oscillation and one canard cycle without head are investigated. Moreover, the one-parameter bifurcation diagram is also presented in this paper through numerical simulations.

In this work, we propose a multidimensional continuum model for plasmid dissemination in biofilms via horizontal gene transfer. The model is formulated as a system of nonlocal partial differential equations derived from mass conservation laws and reaction kinetics principles. Biofilm is modelled as a homogeneous, viscous, incompressible fluid with a velocity given by Darcy’s law. The model considers plasmid-carrying cells as distinct volume fractions and their vertical and horizontal gene transfer via conjugation and natural transformation. The model encompasses local detoxification of biofilm due to plasmid-borne resistance gene and its effect at the community scale. The equations are solved numerically and simulations are performed to investigate how transformation and conjugation regulate the dynamics and the ecology of plasmid spread in both a multidimensional and one-dimensional biofilm system. Model results are able to predict relevant experimentally observed results in plasmid spread, such as the respective intensity of different horizontal gene transfer mechanisms and the importance of selective pressure. Moreover, model results predict coexistence of plasmid-carrying and plasmid-free bacteria even in conditions when one should out-compete the other, offering a simple modelling explanation on global plasmid persistence in bacterial communities.

Quasi-Monte Carlo (QMC) methods have been gaining popularity in computational finance as they are competitive alternatives to Monte Carlo methods that can accelerate numerical accuracy. This paper develops a new approach for reducing the effective dimension combined with a randomized QMC method. A distinctive feature of the proposed approach is its sample-based transformation that enables us to choose a flexible manipulation via regression. In the proposed approach, the first step is to perform a regression using the samples to estimate the parameters of the regression model. An optimal transformation is proposed based on the regression result to minimize the effective dimension. An advantage of this approach is that adopting a statistical approach allows greater flexibility in selecting the regression model. In addition to a linear model, this paper proposes a dimension reduction method based on a linear-quadratic model for regression. In numerical experiments, we focus on pricing different types of exotic options to test the effectiveness of the proposed approach. The numerical results show that different regression models are chosen depending on the underlying risk process and the type of derivative securities. In particular, we show several examples where the proposed method works while existing dimension reductions are ineffective.

Within the context of a two-dimensional framework encompassing interacting species, an examination is conducted in this study on the double Allee effect and prey refuge, considering both species in the interaction. The stability of the feasible equilibrium of the system and diverse bifurcation patterns including codimension-one and codimension-two bifurcations are scrutinized through theoretical and numerical investigations, which reveals the complex dynamics induced by saturated functional response and double Allee effects. Additionally, one-parameter bifurcation diagrams and two-parameter bifurcation diagrams are constructed to intricately evaluate the system’s dynamics indicative of the presence of multiple attractors like bi-stability and tri-stability. Lastly, the sensitivity analysis is performed to delve into the effect of system parameters on species density, which indicates that the parameter $\eta$ proportional to the conversion rate is the most sensitive parameter. A brief discussion further reveals that the model without double Allee effect reduces dynamic complexity.