节点动态增长对复杂网络传输效率的影响研究

在真实的复杂网络中,网络节点会因为网络拓扑结构的变化而增减,进而导致网络节点间传输效率降低.针对这一问题,通过分析复杂网络节点的动态变化,提出网络节点增加的动态传输模型,并利用真实复杂网络的数据模拟仿真,研究网络节点变化对网络传输效率的影响.结果表明:网络的初始大小会随网络节点的动态增加而变化,其传输效率受节点动态增加的影响在最初阶段表现明显,随着节点的继续增加,网络传输效率会趋于平稳,表现出稳定的网络特性.在这个过程中,复杂网络每次新加入节点的个数和节点边维持了网络信息传输的信息量,强化了网络传的输性能,使得网络具有较好的总体控制能力和有效的节点连接方式.     

一个三种群食物链系统的非线性控制

通过非线性控制系统理论研究了一个三种群食物链控制系统正平衡点的稳定性问题.针对不同的输出,分别得到了系统在该点渐近稳定的控制律.对复杂生物系统控制问题的研究具有一定的参考价值.     

年龄结构CD4~+T-细胞模型复杂动力学分析

研究了一类年龄结构的CD4~+T-细胞模型.得到了控制HIV病毒扩散的阈值R_0.当R_01时,无病平衡点全局渐近稳定,病毒在人体内消除;当R_01,且-r+(2αrT~*)/(T_(max))0,地方病平衡点局部渐近稳定,病毒在人体内繁殖;当R_01,且-r+(2αrT~*)/(T_(max))0,系统由感染年龄而产生的复杂动力学行为,如Hopf分支,四周期解及混沌等.最后对模型的复杂动力学行为进行了数值模拟.     

分数阶复杂网络系统的滑模终端控制混沌同步

研究了两类复杂网络混沌系统的终端滑模控制问题,基于分数阶微积分,设计了分数阶非奇异终端滑模面和控制器,给出了严格的数学推理和证明过程,研究表明:适当的控制律下两类复杂网络混沌系统是终端滑模同步的.最后的仿真算例说明方法有效.     

一种双寡头垄断Cournot-Puu模型的混沌控制研究

基于非线性动力学的基本原理,研究了经济系统中的双寡头垄断Cournot-Puu模型及其混沌控制方法.Cournot-Puu模型具有双曲线形需求函数和彼此不同的不变边际成本,离散化的差分系统显示出其复杂的非线性、分岔和混沌行为.在此基础上,结合Cournot-Puu模型的基本特征,应用延迟反馈控制方法以及自适应控制方法对该系统的混沌行为进行了研究.在结合实际经济意义的条件下,对该模型的输出进行调整并实现混沌控制.     

具时滞反馈金融系统的动力学分析与混沌控制

研究了时滞反馈对金融系统的动力学行为的影响.以时滞为分支参数,研究了系统平衡点的局部稳定性,并发现当时滞经过一系列临界值时,系统在平衡点附近经历Hopf分支和Hopf-zero分支.然后,应用规范型方法和中心流形理论得到决定分支周期解性质的详细公式.通过设计合适的反馈增益和时滞,混沌振荡可以控制为稳定的平衡点或周期轨.最后,数值模拟验证了理论结果.     

复杂网络在双曲空间的节点动态择优路径研究

本文研究复杂网络双曲嵌套模型.利用改进克林伯格和克莱尔科夫网络拓扑模型的方法,得到了复杂网络在双曲空间的动态择优路径,推广和发展了复杂网络节点间最优路径的算法.     

Lorenz系统混沌轨道的概率分布特性

利用概率统计方法分析了Lorenz系统混沌轨道的概率分布特性.为研究混沌轨道在系统平衡点处概率分布特性,通过在平衡点处建立超平面,把系统混沌轨道转换为超平面上一系列不动点,然后求得轨道分量的条件概率分布.研究表明混沌轨道在相空间中并不是杂乱无章分布的,在超平面上这些轨道序列主要分布在平衡点两侧,这些轨道点可作为一些混沌控制算法的初始点,有助于提高其收敛效率。     

一类网络速率控制和路由联合算法的稳定性

近年来,动态多路径路由下网络速率控制的研究受到广泛关注.本文提出了一个新的速率控制和多路径路由联合的算法,该算法的特点是具有唯一的平衡点.利用传统的Lyapunov方法,我们证明算法在没有传播时延情形下的全局稳定性.而且,更为重要的是,即使考虑传播时延,在一定的条件下,该算法是局部稳定的.在平衡点处,每条路由上的速率非零.这一事实不但去掉了Kelly F P,Voice T(2005)结果中内部平衡点的假设条件,而且也可以理解为一种探测机制.我们通过仿真证实了算法的正确性,同时仿真结果也表明局部稳定性的吸引域可以很大,甚至是全局稳定的.     

广义不确定系统的终端滑模控制

本文研究了线性广义不确定系统在满足匹配条件下的终端滑模控制的综合设计问题.利用变结构控制方法设计切换函数和终端滑模控制器,获得了在终端滑模控制下,闭环系统的模态在有限时间内到达平衡点的重要结果.克服了传统的变结构控制方法只能保证闭环系统的模态在平衡点渐近稳定,不能实现有限时间到达平衡点的缺点.举例说明了设计方法的合理性和有效性.     

连续型BAM神经网络的指数稳定性

首先将连续型双向联想记忆神经网络转化成一个特殊的Hopfield网络模型.在此基础上,对连续BAM神经网络的指数稳定性进行了新的分析,证明了神经网络连接权矩阵在给定的约束条件下有唯一平衡点.所做的分析可以用于设计全局指数稳定的神经网络.     

Three control strategies for the Lorenz chaotic system

This paper suggests three strategies of the dislocated feedback control, so that enhancing feedback control and speed feedback control of the Lorenz chaotic system to its unstable equilibrium points can be enhanced. When the coefficients of enhancing feedback control and speed feedback control are smaller than those of ordinary feedback control, the complexity and cost of the system control are reduced. Theoretical analysis and numerical simulation are given, revealing the effectiveness of these strategies.     

Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks

In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the global stability of the equilibrium points are discussed by linearization approach of nonlinear systems and Lyapunov function. In the heterogeneous network model, we calculate the basic reproduction number through algebraic method. In addition, Lyapunov functional method and Lasalle invariance principle are applied to study the stability of equilibrium points in the complex network model. Further, we put forward some useful strategies to control the spreading of rumor based on the complex network theory. Finally, we take advantage of numerical simulations to verify the theory above and come up with necessary conclusions.

     

Nonlinear behavior for nanoscale electrostatic actuators with Casimir force

The influence of Casimir force on the nonlinear behavior of nanoscale electrostatic actuators is studied in this paper. A one degree of freedom mass-spring model is adopted and the bifurcation properties of the actuators are obtained. With the change of the geometrical dimensions, the number of equilibrium point varies from zero to two. Stability analysis shows that one equilibrium point is Hopf point and the other is unstable saddle point when there are two equilibrium points. We also obtain the phase portraits, in which the periodic orbits exist around the Hopf point, and a homoclinic orbit passes through the unstable saddle point.     

Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks

In this paper, we study the spreading of infections in complex heterogeneous networks based on an SIRS epidemic model with birth and death rates. We find that the dynamics of the network-based SIRS model is completely determined by a threshold value. If the value is less than or equal to one, then the disease-free equilibrium is globally attractive and the disease dies out. Otherwise, the disease-free equilibrium becomes unstable and in the meantime there exists uniquely an endemic equilibrium which is globally asymptotically stable. A series of numerical experiments are given to illustrate the theoretical results. We also consider the SIRS model in the clustered scale-free networks to examine the effect of network community structure on the epidemic dynamics.     

Approximation on attraction domain of Cohen-Grossberg neural networks

In this paper, approximations of attraction domains of the asymptotically stable equilibrium points of some typical Cohen-Grossberg neural networks are achieved. Most Cohen-Grossberg neural networks are highly nonlinear systems which makes it difficult to approximate their attraction domain. Under some weak assumptions, we are allowed to employ the optimal Lyapunov method to obtain a Lyapunov function for asymptotically stable equilibrium points of a given Cohen-Grossberg neural network. With the help of this Lyapunov function, we approximate the corresponding attraction domain by the iterative expansion approach. Numerical simulations also illustrate that the approximation obtained is really part of the attraction domain.     

Some minimal bimolecular mass-action systems with limit cycles

We discuss three examples of bimolecular mass-action systems with three species, due to Feinberg, Berner, Heinrich, and Wilhelm. Each system has a unique positive equilibrium which is unstable for certain rate constants and then exhibits stable limit cycles, but no chaotic behaviour. For some rate constants in the Feinberg–Berner system, a stable equilibrium, an unstabe limit cycle, and a stable limit cycle coexist. All three networks are minimal in some sense.By way of homogenising these three examples, we construct bimolecular mass-conserving mass-action systems with four species that admit a stable limit cycle. The homogenised Feinberg–Berner system and the homogenised Wilhelm–Heinrich system admit the coexistence of a stable equilibrium, an unstable limit cycle, and a stable limit cycle.     

Chaos control of a fractional order modified coupled dynamos system

This paper analyzes some Routh-Hurwitz stability conditions generalized to the fractional order case, and discusses the stability region of the fractional order system. We analyze the chaotic behavior of the fractional order modified coupled dynamos system concretely, and provide the conditions suppressing chaos to unstable equilibrium points, then use the feedback control method to control chaos in the fractional order modified coupled dynamos system. Numerical simulations show the effectiveness of the method.     

Chaos control of a fractional order modified coupled dynamos system

This paper analyzes some Routh–Hurwitz stability conditions generalized to the fractional order case, and discusses the stability region of the fractional order system. We analyze the chaotic behavior of the fractional order modified coupled dynamos system concretely, and provide the conditions suppressing chaos to unstable equilibrium points, then use the feedback control method to control chaos in the fractional order modified coupled dynamos system. Numerical simulations show the effectiveness of the method.     

Non-autonomous perturbation of autonomous semilinear differential equations: Continuity of local stable and unstable manifolds

In this paper we prove a result on lower semicontinuity of pullback attractors for dynamical systems given by semilinear differential equations in a Banach space. The situation considered is such that the perturbed dynamical system is non-autonomous whereas the limiting dynamical system is autonomous and has an attractor given as union of unstable manifold of hyperbolic equilibrium points. Starting with a semilinear autonomous equation with a hyperbolic equilibrium solution and introducing a very small non-autonomous perturbation we prove the existence of a hyperbolic global solution for the perturbed equation near this equilibrium. Then we prove that the local unstable and stable manifolds associated to them are given as graphs (roughness of dichotomy plays a fundamental role here). Moreover, we prove the continuity of this local unstable and stable manifolds with respect to the perturbation. With that result we conclude the lower semicontinuity of pullback attractors.