CAJ | 학술논문

自适应网络是反映网络动力学和节点动力学相互作用、相互反馈的网络。针对链接重置概率与病毒传播率呈线性正相关关系的自适应网络，建立了基于可变重置概率的自适应网络SIS病毒传播模型的动力学方程。利用非线性微分动力学系统，研究病毒在自适应复杂网络上的传播行为，并通过分析非线性系统对应的雅可比矩阵特征方程，研究系统平衡点的存在条件并对其作稳定性分析。研究发现，当病毒传播阈值R0<1时，系统的无病平衡点局部渐进稳定，不存在地方病平衡点；当病毒传播阈值R0>1时，系统无病平衡点不稳定，存在惟一的地方病平衡点，且该地方病平衡点局部渐进稳定。最后通过数值仿真验证了所得结论的正确性。结果表明，当病毒传播阈值小于1时，病毒将逐渐消亡；当病毒传播阈值大于1时，网络中的病毒将持续传播。
자괄응망락시반영망락동역학화절점동역학상호작용、상호반궤적망락。침대련접중치개솔여병독전파솔정선성정상관관계적자괄응망락，건립료기우가변중치개솔적자괄응망락SIS병독전파모형적동역학방정。이용비선성미분동역학계통，연구병독재자괄응복잡망락상적전파행위，병통과분석비선성계통대응적아가비구진특정방정，연구계통평형점적존재조건병대기작은정성분석。연구발현，당병독전파역치R0<1시，계통적무병평형점국부점진은정，불존재지방병평형점；당병독전파역치R0>1시，계통무병평형점불은정，존재유일적지방병평형점，차해지방병평형점국부점진은정。최후통과수치방진험증료소득결론적정학성。결과표명，당병독전파역치소우1시，병독장축점소망；당병독전파역치대우1시，망락중적병독장지속전파。
The adaptive network is the kind of network that reflects the relation of interaction and mutual feedback between node dynamics and network dynamics. Based on a specific adaptive epidemic spreading model,in which the resetting probability is affected significantly, linearly and positively by the virus transmission rate,a modified susceptible-infected-susceptible epidemic model with varied resetting probability in adaptive networks is presented. Epidemic spreading dynamics is studied by nonlinear differential dynamic system. The exist-ing condition and local stability of the equilibrium in this network model are investigated by analyzing its corresponding characteristic e-quation of Jacobian Matrix of the nonlinear system. It is shown that when the epidemic threshold R0 < 1, the disease-free equilibrium is asymptotically locally stable and endemic equilibrium does not exist. And if R0 > 1,the disease-free equilibrium is not stable and there exists the only asymptotically locally stable endemic equilibrium. Numerical simulations are given to verify the results of theoretical analy-sis. The result shows that when the epidemic threshold is less than 1,the disease will die out,and when the epidemic threshold is greater than 1,the disease will continue to spread in the network.