The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding sto...The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.展开更多
In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained f...In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.展开更多
Risk management often plays an important role in decision making un-der uncertainty.In quantitative risk management,assessing and optimizing risk metrics requires eficient computing techniques and reliable theoretical...Risk management often plays an important role in decision making un-der uncertainty.In quantitative risk management,assessing and optimizing risk metrics requires eficient computing techniques and reliable theoretical guarantees.In this pa-per,we introduce several topics on quantitative risk management and review some of the recent studies and advancements on the topics.We consider several risk metrics and study decision models that involve the metrics,with a main focus on the related com-puting techniques and theoretical properties.We show that stochastic optimization,as a powerful tool,can be leveraged to effectively address these problems.展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
This paper investigates the selective maintenance o systems that perform multi-mission in succession. Selective maintenance is performed on systems with limited break time to improve the success of the next mission. I...This paper investigates the selective maintenance o systems that perform multi-mission in succession. Selective maintenance is performed on systems with limited break time to improve the success of the next mission. In general, the duration of the mission is stochastic. However, existing studies rarely take into account system availability and the repairpersons with different skill levels. To solve this problem, a new multi-mission selective maintenance and repairpersons assignment model with stochastic duration of the mission are developed. To maximize the minimum phase-mission reliability while meeting the minimum system availability, the model is transformed into an optimization problem subject to limited maintenance resources. The optimization is then realized using an analytical method based on a self-programming function and a Monte Carlo simulation method, respectively. Finally, the validity of the model and solution method approaches are verified by numerical arithmetic examples. Comparative and sensitivity analyses are made to provide proven recommendations for decision-makers.展开更多
This paper proposes a reliability evaluation model for a multi-dimensional network system,which has potential to be applied to the internet of things or other practical networks.A multi-dimensional network system with...This paper proposes a reliability evaluation model for a multi-dimensional network system,which has potential to be applied to the internet of things or other practical networks.A multi-dimensional network system with one source element and multiple sink elements is considered first.Each element can con-nect with other elements within a stochastic connection ranges.The system is regarded as successful as long as the source ele-ment remains connected with all sink elements.An importance measure is proposed to evaluate the performance of non-source elements.Furthermore,to calculate the system reliability and the element importance measure,a multi-valued decision diagram based approach is structured and its complexity is analyzed.Finally,a numerical example about the signal transfer station system is illustrated to analyze the system reliability and the ele-ment importance measure.展开更多
The present work investigates higher order stress,strain and deformation analyses of a shear deformable doubly curved shell manufactures by a Copper(Cu)core reinforced with graphene origami auxetic metamaterial subjec...The present work investigates higher order stress,strain and deformation analyses of a shear deformable doubly curved shell manufactures by a Copper(Cu)core reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads.The effective material properties of the graphene origami auxetic reinforced Cu matrix are developed using micromechanical models cooperate both material properties of graphene and Cu in terms of temperature,volume fraction and folding degree.The principle of virtual work is used to derive governing equations with accounting thermal loading.The numerical results are analytically obtained using Navier's technique to investigate impact of significant parameters such as thermal loading,graphene amount,folding degree and directional coordinate on the stress,strain and deformation responses of the structure.The graphene origami materials may be used in aerospace vehicles and structures and defence technology because of their low weight and high stiffness.A verification study is presented for approving the formulation,solution methodology and numerical results.展开更多
We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution co...We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.展开更多
基金Supported by the National Natural Science Foundation of China(10671182)。
文摘The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.
基金Supported by the National Natural Science Foundation of China(11971458,11471310)。
文摘In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.
文摘Risk management often plays an important role in decision making un-der uncertainty.In quantitative risk management,assessing and optimizing risk metrics requires eficient computing techniques and reliable theoretical guarantees.In this pa-per,we introduce several topics on quantitative risk management and review some of the recent studies and advancements on the topics.We consider several risk metrics and study decision models that involve the metrics,with a main focus on the related com-puting techniques and theoretical properties.We show that stochastic optimization,as a powerful tool,can be leveraged to effectively address these problems.
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
文摘This paper investigates the selective maintenance o systems that perform multi-mission in succession. Selective maintenance is performed on systems with limited break time to improve the success of the next mission. In general, the duration of the mission is stochastic. However, existing studies rarely take into account system availability and the repairpersons with different skill levels. To solve this problem, a new multi-mission selective maintenance and repairpersons assignment model with stochastic duration of the mission are developed. To maximize the minimum phase-mission reliability while meeting the minimum system availability, the model is transformed into an optimization problem subject to limited maintenance resources. The optimization is then realized using an analytical method based on a self-programming function and a Monte Carlo simulation method, respectively. Finally, the validity of the model and solution method approaches are verified by numerical arithmetic examples. Comparative and sensitivity analyses are made to provide proven recommendations for decision-makers.
基金supported by the National Natural Science Foundation of China(72101025,72271049),the Interdisciplinary Research Project for Young Teachers of USTB(Fundamental Research Funds for the Central Universities,FRF-IDRY-24-024)the Hebei Natural Science Foundation(F2023501011)+1 种基金the Fundamental Research Funds for the Central Universities(FRF-TP-20-073A1)the R&D Program of Beijing Municipal Education Commission(KM202411232015).
文摘This paper proposes a reliability evaluation model for a multi-dimensional network system,which has potential to be applied to the internet of things or other practical networks.A multi-dimensional network system with one source element and multiple sink elements is considered first.Each element can con-nect with other elements within a stochastic connection ranges.The system is regarded as successful as long as the source ele-ment remains connected with all sink elements.An importance measure is proposed to evaluate the performance of non-source elements.Furthermore,to calculate the system reliability and the element importance measure,a multi-valued decision diagram based approach is structured and its complexity is analyzed.Finally,a numerical example about the signal transfer station system is illustrated to analyze the system reliability and the ele-ment importance measure.
基金supported by Scientific Research Project of Qiqihar University(145209130)supported by the Natural Science Foundation of Inner Mongolia Autonomous Region of China(Grant No.2023LHMS05054 and 2023LHMS05017)+3 种基金the Inner Mongolia University of Technology Natural Science Foundation of China(Grant No.DC2200000903)the Program for Innovative Research Teams in Universities of the Inner Mongolia Autonomous Region of China(Grant No.NMGIRT2213)the key technological project of Inner Mongolia(Grant No.2021GG0255 and 2021GG0259)the Fundamental Research Funds for the directly affiliated Universities of Inner Mongolia Autonomous Region(Grant No.JY20220046)。
文摘The present work investigates higher order stress,strain and deformation analyses of a shear deformable doubly curved shell manufactures by a Copper(Cu)core reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads.The effective material properties of the graphene origami auxetic reinforced Cu matrix are developed using micromechanical models cooperate both material properties of graphene and Cu in terms of temperature,volume fraction and folding degree.The principle of virtual work is used to derive governing equations with accounting thermal loading.The numerical results are analytically obtained using Navier's technique to investigate impact of significant parameters such as thermal loading,graphene amount,folding degree and directional coordinate on the stress,strain and deformation responses of the structure.The graphene origami materials may be used in aerospace vehicles and structures and defence technology because of their low weight and high stiffness.A verification study is presented for approving the formulation,solution methodology and numerical results.
基金Supported by the Science and Technology Research Projects of Hubei Provincial Department of Education(B2022077)。
文摘We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.
