概周期时标理论及若干应用研究

发布时间：2018-05-01 19:14

本文选题：时标上的动力方程 + 概周期时标　；参考：《云南大学》2016年博士论文

【摘要】：本文提出了概周期时标,时标上的概周期函数,时标上的概自守函数等的一些新定义,并给出了这些新的概周期时标和概周期时标上的概周期函数和概自守函数的一些基本性质.我们证明了：若与线性非齐次动力方程对应的齐次方程容许指数二分,则非齐次概周期或概自守动力方程有概周期解或概自守解.作为本文结果的应用：(ⅰ)我们证明了时标上一类具时变时滞的分流抑制细胞神经网络的概自守解的存在性和全局指数稳定性.我们得到的关于时标上该类神经网络的结果对于微分方程(时标T=R)和差分方程(时标T=Z)情形也是最新的.(ⅱ)我们得到了时标上一类Nicholson's blowflies模型的正概周期解存在并指数稳定的充分条件,我们的结果即使当时标T=R和T=Z时也是新的,同时改进一些相应的已知结果.我们的结论表明：在满足一个简单条件下,连续时间的Nicholson's blowflies模型和与其类似的离散时间模型有相同的动力学行为.我们也给出数值例子来说明所得结果的有效性.(ⅲ)我们证明了时标上一类具混合时变时滞和连接项时滞的中立型竞争神经网络的概周期解的存在性和全局指数稳定性.我们得到的关于这类中立型竞争神经网络的结果是全新的,我们也给出了数值例子来说明所得结果的可行性.
[Abstract]:In this paper, some new definitions of almost periodic time scale, almost periodic function on time scale, almost self-defending function on time scale, etc. Some basic properties of almost periodic functions and almost self-defensive functions on these new almost periodic scalars and almost periodic time scales are given. We prove that if the homogeneous equation corresponding to the linear inhomogeneous dynamical equation is admissible exponential dichotomy, then the inhomogeneous almost periodic or almost self-preserving dynamic equation has almost periodic solution or almost self-conformal solution. As an application of the results in this paper, we prove the existence and global exponential stability of almost self-defensive solutions for a class of shunt suppression cellular neural networks with time-varying delays on time scales. The results obtained for this kind of neural networks on time scales are also the latest. (II) We obtain the existence of positive almost periodic solutions for a class of Nicholson's blowflies models on time scales for the case of differential equations (TX R) and difference equations (time scales TJ Z). (2) We obtain the existence of positive almost periodic solutions for a class of Nicholson's blowflies models on time scales. Sufficient conditions for exponential stability, Our results are new even when we mark TX R and TX Z, and some known results are improved at the same time. Our results show that the Nicholson's blowflies model with continuous time has the same dynamic behavior as the discrete-time model under a simple condition. We also give a numerical example to illustrate the validity of the obtained results. (III) We prove the existence of almost periodic solutions and the global exponential stability of a class of neutral competitive neural networks with mixed time-varying delays and connection-term delays on time scales. The results obtained for this kind of neutral competitive neural networks are completely new. We also give numerical examples to illustrate the feasibility of the obtained results.
【学位授予单位】：云南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O175

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