This paper presents an advanced mathematical framework for modeling com-bat dynamics between two opposing forces using nonlinear reaction-diffusion equations.Extending classical Lanchester models,we incorporate spatia...This paper presents an advanced mathematical framework for modeling com-bat dynamics between two opposing forces using nonlinear reaction-diffusion equations.Extending classical Lanchester models,we incorporate spatially de-pendent diffusion coefficients to capture modern battlefield complexities.A robust numerical scheme based on the Alternating Direction Implicit(ADI)method is developed,ensuring stability and second-order accuracy in spatio-temporal discretization.The model integrates logistic growth,combat attri-tion,and tactical diffusion processes,validated through analytical bench-marks.Simulations reveal intricate pattern formation,transient dynamics,and boundary adherence,demonstrating applicability to military strategy op-timization.The complete formulation and numerical implementation are thoroughly discussed,providing insights into nonlinear system behavior un-der varying tactical conditions.展开更多
Lanchester equations and their extensions are widely used to calculate attrition in warfare models. The current paper addresses the warfare command decision-making problem for winning when the total combats capability...Lanchester equations and their extensions are widely used to calculate attrition in warfare models. The current paper addresses the warfare command decision-making problem for winning when the total combats capability of the attacking side is not superior to that of the defending side. For this problem, the corresponding warfare command stratagems, which can transform the battlefield situation, are proposed and analyzed quantitatively by considering the influence of the warfare information factor. The application examples in military conflicts show the feasibility and effectiveness of the proposed model and the warfare command stratagems for winning. The research results may provide a theoretical reference for warfare command decision making.展开更多
文摘This paper presents an advanced mathematical framework for modeling com-bat dynamics between two opposing forces using nonlinear reaction-diffusion equations.Extending classical Lanchester models,we incorporate spatially de-pendent diffusion coefficients to capture modern battlefield complexities.A robust numerical scheme based on the Alternating Direction Implicit(ADI)method is developed,ensuring stability and second-order accuracy in spatio-temporal discretization.The model integrates logistic growth,combat attri-tion,and tactical diffusion processes,validated through analytical bench-marks.Simulations reveal intricate pattern formation,transient dynamics,and boundary adherence,demonstrating applicability to military strategy op-timization.The complete formulation and numerical implementation are thoroughly discussed,providing insights into nonlinear system behavior un-der varying tactical conditions.
基金partially supported by the National Natural Science Foundation of China under Grant No 60774097 and 11171301by the Fundamental Research Funds for the Central Universities under Grant No N100604019
文摘Lanchester equations and their extensions are widely used to calculate attrition in warfare models. The current paper addresses the warfare command decision-making problem for winning when the total combats capability of the attacking side is not superior to that of the defending side. For this problem, the corresponding warfare command stratagems, which can transform the battlefield situation, are proposed and analyzed quantitatively by considering the influence of the warfare information factor. The application examples in military conflicts show the feasibility and effectiveness of the proposed model and the warfare command stratagems for winning. The research results may provide a theoretical reference for warfare command decision making.
