基于区间系统理论的分数阶混沌系统同步

通过设计一个非线性反馈控制器,实现了分数阶混沌系统的同步.与其他的分数阶混沌系统同步方法相比,提出的控制器设计方法保留了部分误差系统中的非线性项,而没有完全抵消同步误差系统的非线性项,有效改善了误差系统的控制性能.同时,应用区间分数阶线性时不变系统稳定性原理和线性矩阵不等式技术,得到了一个新的分数阶混沌系统同步的充分条件,进而获得的控制器保证了混沌系统同步.仿真结果验证了提出方法的有效性. 关键词： 区间分数阶时不变系统 分数阶混沌系统 混沌同步     

Comment on “A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family”, P. Yu,X.X. Liao,S.L. Xie,Y.L. Fu [Commun Nonlinear Sci Numer Simulat 14 (2009) 2886–2896]

In the commented paper the authors study some aspects of boundedness in the general Lorenz family, $\dot{x}=\sigma (y-x)\text{,}\dot{y}=\rho x-\gamma y-\mathit{xz}\text{,}\dot{z}=-\beta z+\mathit{xy}$, considering that it contains four independent parameters. However, as we show here by means of a linear scaling in time and coordinates, they are dealing with a system homothetically equivalent to the Lorenz system. Consequently, the novel and interesting results they provide for the general Lorenz family can be obtained working directly with the Lorenz equations, that is, dealing only with three independent parameters.     

Parameter space of the Rulkov chaotic neuron model

The parameter space of the two dimensional Rulkov chaotic neuron model is taken into account by using the qualitative analysis, the co-dimension 2 bifurcation, the center manifold theorem, and the normal form. The goal is intended to clarify analytically different dynamics and firing regimes of a single neuron in a two dimensional parameter space. Our research demonstrates the origin that there exist very rich nonlinear dynamics and complex biological firing regimes lies in different domains and their boundary curves in the two dimensional parameter plane. We present the parameter domains of fixed points, the saddle-node bifurcation, the supercritical/subcritical Neimark–Sacker bifurcation, stability conditions of non hyperbolic fixed points and quasiperiodic solutions. Based on these parameter domains, it is easy to know that the Rulkov chaotic neuron model can produce what kinds of firing regimes as well as their transition mechanisms. These results are very useful for building-up a large-scale neuron network with different biological functional roles and cognitive activities, especially in establishing some specific neuron network models of neurological diseases.     

Chaotic fractional‐order model for muscular blood vessel and its control via fractional control scheme

This article studies the chaotic and complex behavior in a fractional‐order biomathematical model of a muscular blood vessel (MBV). It is shown that the fractional‐order MBV (FOMBV) model exhibits very complex and rich dynamics such as chaos. We show that the corresponding maximal Lyapunov exponent of the FOMBV system is positive which implies the existence of chaos. Strange attractors of the FOMBV model are depicted to validate the chaotic behavior of the system. We change the fractional order of the model and investigate the dynamics of the system. To suppress the chaotic behavior of the model, we propose a single input fractional finite‐time controller and prove its stability using the fractional Lyapunov theory. In addition, the effects of the model uncertainties and external disturbances are taken into account and a robust fractional finite‐time controller is constructed. The upper bound of the chaos suppression time is also given. Some computer simulations are presented to illustrate the findings of this article. © 2014 Wiley Periodicals, Inc. Complexity 20: 37–46, 2014     

基于动态模态分解的长江口海表温度时空分布特征重构研究

河口近海海域的海表温度分布特征对于深入理解海洋热力、动力过程及海气相互作用等自然过程及综合效应具有重要意义。卫星数据重构是精确获取动态大面积海表温度数据的重要手段,采用非线性系统的动态模态分解（dynamic mode decomposition,DMD）数据分析方法,利用2003年1月至2016年7月的MODIS\SST数据,经剔除异常数据、填补空白数据后,重构了2016年8月至2019年12月长江口海洋表面温度数据,并评估了重构效果。研究结果表明,在时序数据充足的情况下,DMD算法能很好地解决动态系统的采样问题。DMD结合正交三角（orthogonal right triangular,QR）分解算法能有效重构长江口的海表温度数据,平均均方根误差（root mean square error,RMSE）为0.007 6。进一步分析发现,无论是DMD算法还是DMD结合QR分解算法,还原结果精度都较高。     

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015     

Impulsive synchronization of time delay bursting neuron systems with unidirectional coupling

In the article, impulsive synchronization of chaotic bursting in Hindmarsh–Rose neuron systems with time delay via partial state signal is investigated. Based on impulsive control theory of dynamical systems, the sufficient conditions on feedback strength and impulsive interval are established to guarantee the synchronization. Numerical simulations show the effectiveness of the proposed scheme. The obtained results may be helpful to understand dynamical mechanism of signal transduction in real neuronal activity. © 2014 Wiley Periodicals, Inc. Complexity 21: 38–46, 2015     

Creating new stable periodic orbit by small region feedback control

In this paper an important problem in chaos control theory concerningthe possibility of generating a new stable periodic solutionby a small feedback control law for a dynamical system is addressed.It is proved that a solution with an initial point being somekind of non-wandering property can become a new asymptoticallystable solution by a small feedback control law. This showsthat the popular opinion that a small control law is not ableto create a new periodic point is untrue, and suggests a newapproach to controlling chaos.     

统一混沌系统的耦合同步

对线性耦合的两个统一混沌系统同步进行研究.基于线性时变连续系统的稳定性理论，得到初始值不同的两个统一混沌系统全局渐进同步的一种新的充分条件.另外，与已经提出的判定统一混沌系统同步的方法进行比较，发现这里得到的充分条件的约束关系少、缺少保守性，而且满足的耦合系数范围更广.将该方法应用于统一混沌系统，数值仿真表明了该法的有效性与可行性. 关键词： 统一混沌系统 耦合同步 线性时变连续系统