Hindmarsh-Rose神经模型的混沌控制

应用稳定性准则的混沌控制方法控制单个Hindmarsh-Rose神经元模型的混沌发放峰序列和混沌爆发运动。通过对膜电压的非线性连续-时间反馈干扰的输入,将混沌运动控制到5峰／爆发（5spikes/burst）轨道上,该轨道嵌入在混沌吸引子内。数值模拟结果显示该方法在控制HR神经元模型方面是有效的。     

具有共生作用两种群离散耦合Logistic模型混沌控制

针对具有共生作用的离散耦合Logistic模型,首先采用Lyapunov指数方法验证了混沌现象的存在.然后详细地分析了系统随参数变化的分岔图,发现了系统中存在更复杂的现象.最后应用混沌跟踪控制方法控制系统的混沌现象,使得种群稳定到正不动点轨道上,消除了种群中存在的混沌现象.仿真结果验证了控制方法的有效性.     

离散广义Logistic模型的混沌控制

利用Lyapunov指数方法,验证了一类离散广义Logistic模型存在混沌现象,并采用混沌控制中OGY方法的基本思想,研究了这类模型的混沌控制问题,得出了消除混沌,保持种群稳定到不动点和2-周期轨道的充分条件．     

肝炎和伤寒流行过程的混沌分维研究

以辽宁省本溪市１９５５－１９９６年的肝炎、伤寒逐月发病的数据为根据，利用混沌动力学中“相空间技术”，对流行病过程进行能量谱分析及混沌分析。发现伤寒的流行过程是混沌的，混沌迭代模型是Ｘｔ＋１＝ｒＸｔｅｘｐ｛－０．０００９２８７（Ｘｔ－３３．２５３３２）＾２｝；肝炎的流行过程是非混沌的。在模型参数变化范围内，经历了周期状态、混沌状态之间的转换，这表明伤寒的流行过程是复杂的，给出了流行病的“阈值”，以控制它们的流行涨落，求出伤寒的关联分维是３．０８７。     

肌型血管生物数学模型的自适应Backstepping控制设计

提出了基于Backstepping自适应控制方法研究医学上容易引发心肌梗塞等疾病的血管痉挛,即肌型血管生物数学模型的受控问题．设计了一个自适应控制器,使系统的状态量都渐近稳定到0,并使系统全局稳定,从理论上得出处于混沌运动状态的血管能趋于正常化,对有效防治和治疗心肌梗塞等疾病具有重要的意义．最后的仿真结果表明了此方法在理论上的有效性．     

一类离散捕食-食饵模型的混沌跟踪控制

针对一类离散捕食食饵系统,采用Lyapunov指数方法、绘制系统分岔图和混沌吸引子等方式验证了混沌现象的存在.为了消除系统的混沌现象,根据控制理论的轨迹跟踪控制原理,设计混沌跟踪控制器将系统控制到任意给定的期望周期轨道上,达到了稳定种群的目的.仿真分析表明了所设计控制器的有效性.     

可兴奋细胞CHAY模型的混沌控制

对可兴奋细胞的Ｃｈａｙ模型的混沌解进行控制。控制的方法为：（１）参数周期扰动;（２）周期激励;（３）周期脉冲（拍）激励。用这三种方法都实现了把混沌转化为周期运动。     

具有潜伏和隔离的传染病模型的全局稳定性

研究了一类具有隔离仓室和潜伏仓室的非线性高维自治微分系统SEQIJR传染病模型,得到疾病绝灭与否的阀值一基本再生数R0．证明了当R0≤1时,模型仅存在无病平衡点,且无病平衡点是全局渐近稳定的,疾病最终绝灭;当R0〉1时,模型存在两个平衡点,无病平衡点不稳定,地方病平衡点全局渐近稳定,疾病将持续．隔离措施影响着基本再生数,进而推得结论：适当地增大隔离强度,将有益于有效地控制疾病的蔓延．这就从理论上揭示了隔离对疾病控制的积极作用．     

电突触耦合Chay神经元同步振荡的研究

从微观解释异常神经元构建组织时癫痫样波形的相互制约关系对神经系统疾病的研究很有意义,而两神经元耦合特性的探索是重要的基础工作。采用Chay提供的Pacemaker神经元模型以电突触耦合来研究不同耦合强度对神经元动态时序的影响,并指出突触作用过程的混沌特征。给出并讨论了不同状态神经元相耦合时非线性振荡的数值计算结果,即：起搏神经元与处于冲动混沌状态神经元、处于冲动混沌和独态冲动状态的异常神经元、异常神经元与处于静息状态神经元的动态时序,还给出了部分相图以及Ca 离子浓度变化的特点。神经元这种负载特性的讨论有助于研究在活组织中癫痫发作的机理、传输和控制。     

再生数R0的计算及其控制策略

在传染病数学模型中,一般有一个传染病消除平衡点和至少一个地方病平衡点,这些平衡点的稳定性由再生数R_0决定,当R_0<1,疾病消除平衡点稳定,此传染病可以消除;当R_0>1,疾病消除平衡点不稳定,此传染病将蔓延,所以再生数R_0是传染病数学模型中最重要的参数.本文针对乙型肝炎病毒的传播方式以及各种状态间的转化模式建立了乙型肝炎数学模型,并利用马尔可夫链的方法计算乙型肝炎数学模型中的再生数R_0,提出了通过采取降低R_0的方法对乙型肝炎数学模型施加有效控制的策略.     

Melnikov analysis of chaos in a simple epidemiological model

 Melnikov’s method is applied to an SIR model of epidemic dynamics with a periodically modulated nonlinear incidence rate. This analysis establishes mathematically, for the first time, the existence of chaotic motion in these models. A related technique also makes it possible to prove that homoclinic bifurcations occurs in the model. Received 8 August 1995; received in revised form 21 November 1995     

Invasion dynamics of epidemic with the Allee effect

Investigating the likely success of epidemic invasion is important in the epidemic management and control. In the present study, the invasion of epidemic is initially introduced to a predator-prey system, both species of which are considered to be subject to the Allee effect. Mathematically, the invasion dynamics is described by three nonlinear diffusion-reaction equations and the spatial implicit and explicit models are designed. By means of extensive numerical simulations, the results of spatial implicit model show that the Allee effect has an opposite impact on the invasion criteria and local dynamics when that on the different species. As the intensity of the Allee effect increases, the domain of epidemic invasion reduces and the system dynamics is changed from the stable state to the limit cycle and finally becomes the chaotic state when the susceptible prey with the Allee effect, but the domain expands and the system dynamics is changed from limit cycle to a table point when the predator is subject to the Allee effect. Results from the spatial explicit model show that the strong intensity of the Allee effect can lead to the catastrophic global extinction of all species in the case of that on the susceptible prey. While the predator with the Allee effect, the increased intensity of which makes spatial species reach a stable state. Furthermore, numerical simulations reveal a certain relationship between the invasion speed and spatial patterns.     

Modeling and real-time prediction of classical swine fever epidemics

We propose a new method to analyze outbreak data of an infectious disease such as classical swine fever. The underlying model is a two-type branching process. It is used to deduce information concerning the epidemic from detected cases. In particular, the method leads to prediction of the future course of the epidemic and hence can be used as a basis for control policy decisions. We test the model with data from the large 1997-1998 classical swine fever epidemic in The Netherlands. It turns out that our results are in good agreement with the data.     

Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

Chaotic dynamics introduced in a recurrent neural network model is applied to controlling an object to track a moving target in two-dimensional space, which is set as an ill-posed problem. The motion increments of the object are determined by a group of motion functions calculated in real time with firing states of the neurons in the network. Several cyclic memory attractors that correspond to several simple motions of the object in two-dimensional space are embedded. Chaotic dynamics introduced in the network causes corresponding complex motions of the object in two-dimensional space. Adaptively real-time switching of control parameter results in constrained chaos (chaotic itinerancy) in the state space of the network and enables the object to track a moving target along a certain trajectory successfully. The performance of tracking is evaluated by calculating the success rate over 100 trials with respect to nine kinds of trajectories along which the target moves respectively. Computer experiments show that chaotic dynamics is useful to track a moving target. To understand the relations between these cases and chaotic dynamics, dynamical structure of chaotic dynamics is investigated from dynamical viewpoint.     

Chaotic neural network applied to two-dimensional motion control

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.     

Pulse vaccination strategy in the SIR epidemic model

Theoretical results show that the measles ‘pulse’ vaccination strategy can be distinguished from the conventional strategies in leading to disease eradication at relatively low values of vaccination. Using the SIR epidemic model we showed that under a planned pulse vaccination regime the system converges to a stable solution with the number of infectious individuals equal to zero. We showed that pulse vaccination leads to epidemics eradication if certain conditions regarding the magnitude of vaccination proportion and on the period of the pulses are adhered to. Our theoretical results are confirmed by numerical simulations. The introduction of seasonal variation into the basic SIR model leads to periodic and chaotic dynamics of epidemics. We showed that under seasonal variation, in spite of the complex dynamics of the system, pulse vaccination still leads to epidemic eradication. We derived the conditions for epidemic eradication under various constraints and showed their dependence on the parameters of the epidemic. We compared effectiveness and cost of constant, pulse and mixed vaccination policies.     

SIS epidemic attractors in periodic environments

The demographic dynamics are known to drive the disease dynamics in constant environments. In periodic environments, we prove that the demographic dynamics do not always drive the disease dynamics. We exhibit a chaotic attractor in an SIS epidemic model, where the demograhic dynamics are asymptotically cyclic. Periodically forced SIS epidemic models are known to exhibit multiple attractors. We prove that the basins of attraction of these coexisting attractors have infinitely many components.