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Differential game-based analysis of multi-attacker multi-defender interaction

Science China(Information Sciences) 2021年第12期64卷 202-214页

作者： Qiuyue GAO Huici WU Yunfei ZHANG Xiaofeng TAO National Engineering Laboratory for Mobile Network Technologies Beijing University of Posts and Telecommunications

Due to the increasing number of wireless terminals and progressively extensive interconnections among them, interaction between the attack group and defense group is becoming a dominant security manifestation in future wireless networks. This paper focuses on the modeling and analysis of multi-attacker to multi-defender interaction. First, considering the continuous interaction between the attack group and defense group in real-time, a differential game-based multi-attacker to multi-defender interaction model is explicated with paralysis threshold introduced to reduce the ping-pong effect in paralysis. Optimal control theory is then introduced to obtain the equilibrium strategy with hamilton best control method and a proposed optimal strategy selection algorithm for multi-attacker to multi-defender interaction. Finally, simulations are provided to demonstrate the evolutionary trajectory of optimal attack and defensive strategies and the relationship between the paralysis threshold and the group strength evolution results. Numerical results show the attackers and defenders are aggressive to strengthen their groups initially and then gradually decrease their strength to obtain ideal cost-effectiveness ratios. Moreover, increasing the defense paralysis threshold within a certain range will be more conducive to improving the defense effectiveness.

关键词： differential game multi-attacker to multi-defender interaction optimal control theory hamilton function equilibrium strategy

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Higher-Order Lagrangian Equations of Higher-Order Motive Mechanical System

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Communications in Theoretical Physics 2008年第2期49卷 479-481页

作者： ZHAO Hong-Xia MA Shan-Jun SHI Yong College of Physics and Communication Electronics Jiangxi Normal University Nanchang 330022 China

In this paper, if the condition of variation δt = 0 is satisfied, the higher-order Lagrangian equations and higher-order hamilton＇s equations, which show the consistency with the results of traditional analytical mechanics, are obtained from the higher-order Lagrangian equations and higher-order hamilton＇s equations. The results can enrich the theory of analytical mechanics.

关键词： higher-order Lagrange function hamilton function higher-order Lagrangian equation

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HEAT SOURCE-INFLUENCED FINITE AMPLITUDE ULTRALONG WAVE

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Acta meteorologica Sinica 1994年第1期8卷 9-18页

作者：何建中章基嘉 Nanjing Institute of Meteorology Nanjing 210044 Chinese Academy of Meteorological Sciences Beijing 100081

Discussed in this paper is finite amplitude ultralong wave under the influence of heat *** conditions are first investigated for the existence of periodic and solitary ultralong waves of finite amplitude in the Burger model with the aid of hamilton function and variation of total energy and then the wave analytical expression is formulated by means of the functional approximation and the hamilton function as the motion invariant in *** show that the finite amplitude ultralong wave influenced by heat sources is unlikely to generate a solitary wave solution and im- poses no constraints on horizontal divergence as opposed to the case with the effect of heat sources available.

关键词： hamilton function finite amplitude ultralong wave heat source

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