Kolmogorov流动模型的七模截断及其混沌特性

为了给出Kolmogorov流动模型中混沌行为的数学描述,选取常数k=3,重新对描述该模型的Navier-Stokes方程进行截断,得到了一个新的七维混沌系统．数值模拟了控制参数在一定范围内变化时方程组的基本动力学行为和混沌轨线,分析了其混沌特性．一方面证实了具有湍流特性的数学对象归因于低维混沌吸引子,另一方面有利于更好地了解湍流流动产生的机理.     

二维耦合Logistic映射的动力学性质及在流密码生成中的应用

本文研究了带二次耦合项的二维Logistic映射的性质和分岔行为,数值模拟了混沌的生成过程．若控制一个参数值近似为1,则产生近乎满的混沌区．这种混沌区产生的随机序列所生成的流密码具有很好的0-1分布、高线性复杂性、密钥敏感性等．最后给出了用于保密通信的模型．     

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.     

耦合混沌Hindmarsh-Rose神经元系统中相互作用诱导的周期解研究

神经元细胞作为构成神经系统结构和功能的基本单位,在神经信号传输过程中具有非常重要的作用.采用Hindmarsh-Rose神经元模型,探究与细胞中钙离子浓度有关的一个恢复变量参数在神经元信号传递中的影响.研究表明,当改变恢复变量参数值时,单个神经元会出现周期或混沌的放电行为,并且对该参数值变化比较敏感.此外,当单个神经元为混沌放电时,随着相互作用强度的变化,耦合神经元系统不仅会出现混沌放电行为,还会产生周期放电行为,周期解窗口和混沌解窗口交替出现.当恢复变量参数值不同时,周期解窗口的个数和周期解的性质明显不同.该结论表明,该恢复变量参数在调控神经元混沌放电和周期放电行为过程中扮演着非常重要的角色.     

延迟有限理性下推测变差寡头博弈模型的复杂性

在参与人具有延迟有限理性决策下,构造含有伯川德推测变差的动态寡头模型,对模型的推测变差均衡点的存在性和唯一性进行了证明,把企业的产量调整速度作为变量,分析企业的产量调整速度的变化产生的周期分岔、混沌等复杂行为,并对比了延迟理性和DFC方法的混沌控制效果.研究表明,尽管二者作用机理不同,但混沌现象都发生了延迟甚至消失,即系统的稳定性增强.     

一类基于排斥吸引函数的离散混沌模型

利用排斥吸引函数容易实现有界离散映射的特点,提出了一类新的离散混沌映射,并利用理论推导对其分岔机理进行了研究.通过分岔图和Lyapunov指数谱清楚地展示了这个离散映射从有序到混沌的变化过程.可以看到这个简单的排斥吸引函数也能够象著名的Logistic模型一样产生复杂的动力学行为.     

通过同步实现从混沌到有序的转变

本文旨在研究连续的混沌系统是否存在“混沌＋混沌=有序”的现象．证明了两个双向耦合的连续混沌系统在一些情况下可产生有序的动力学行为．作为例子，通过选取适当的耦合参数使Lorenz系统以及Chen和Lee引入的混沌系统同步，进而对同步系统的动力学行为进行了理论分析和数值模拟．结果表明，逐渐改变参数，系统实现了从混沌到有序的过渡．     

动力系统实测数据的非线性混沌模型重构

动力系统实测非线性混沌数据的模型重构技术是相空间重构的重要内容。在判定了实测数据的非线性混沌特征,计算了实测数据的分维数,Lyapunov指数,并对其进行了本征值分解和噪声去除及确定其模型阶数以后,提出了一个动力系统实测数据的非线性混沌模型,给出了相应的模型参数辨识方法,并用其确立的混沌模型进行了预测工作,计算结果表明:模型参数辨识方法能迅速地将参数估计值带到多峰目标函数的全局最少值附近,然后再采用优化理论能较准确地求出模型的参数,用得到的混沌模型对系统进行预测工作其预测效果良好,且混沌时序不可能作长期预测。     

两自由度非线性振动系统主参数激励下的分岔分析

本文给出了参数激励作用下两自由度非线性振动系统,在1:2内共振条件下主参数激励低阶模态的非线性响应.采用多尺度法得到其振幅和相位的调制方程,分析发现平凡解通过树枝分岔产生耦合模态解,采用Melnikov方法研究全局分岔行为,确定了产生Smale马蹄型混沌的参数值.     

平面不可压缩Navier-Stokes方程五模系统的力学机理及能量演化

该文研究了平面不可压缩Navier-Stokes方程五模系统的力学机理及能量演化问题,通过将五模混沌系统转换成Kolmogorov形系统,把系统的力矩分为三种类型:惯性力矩,耗散力矩和外力矩.通过不同力矩的结合分析和研究了系统产生混沌的关键因素和物理意义.讨论了能量与雷诺数之间的关系.研究表明三种力矩的耦合是产生混沌的必要条件,而且只有耗散力矩和驱动力矩(外力矩)相匹配时,系统才能产生混沌,其中任何两种力矩耦合均不可能产生混沌.外力矩给系统提供能量,导致系统失稳出现分岔与混沌.引进Casimir函数分析系统的动力学行为和能量演化,并估计混沌吸引子的界.Casimir函数反映了能量转换和轨道与平衡点间的距离.     

Bifurcation and nonsmooth dynamics of solitary waves in the generalized long-short wave equations

Generalized wave equations, which model the resonant interaction between the long wave and the short wave, are considered. To understand the underlying complex dynamics, the bifurcations and nonsmooth behaviors of solitary waves for this system are investigated by qualitative techniques in dynamical systems. These complex behaviors may serve as mechanisms for fascinating physical phenomena such as solitons, chaos and turbulence.     

Chaos control applied to heart rhythm dynamics

The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic, being respectively related to normal and pathological physiological functioning. In this regard, chaos control methods may be useful to promote the stabilization of unstable periodic orbits using small perturbations. In this article, the extended time-delayed feedback control method is applied to a natural cardiac pacemaker described by a mathematical model. The model consists of a modified Van der Pol equation that reproduces the behavior of this pacemaker. Results show the ability of the chaos control strategy to control the system response performing either the stabilization of unstable periodic orbits or the suppression of chaotic response, avoiding behaviors associated with critical cardiac pathologies.     

Nonlinear dynamics and chaos in a fractional-order financial system

This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found.     

多级混沌映射变参数伪随机序列产生方法研究

针对单混沌系统因计算机有限精度效应产生的混沌退化问题,提出了一种多级混沌映射变参数伪随机序列产生方法,基于该方法构建的混沌系统较单混沌系统具有伪随机序列周期大,密钥数量多,密钥空间大等优势,所产生的密码具有更高的安全性能.仿真结果表明,该方法在低复杂度条件下可以生成大量具有良好自相关和互相关特性的混沌序列,在安全领域具有良好的应用前景.     

Bifurcations and chaos in Mira 2 map

In this paper, Mira 2 map is investigated. The conditions of the existence for fold bifurcation, flip bifurcation and Naimark-Sacker bifurcation are derived by using center manifold theorem and bifurcation theory. And the conditions of the existence for chaos in the sense of Marroto are obtained. Numerical simulation results not only show the consistence with the theoretical analysis but also display complex dynamical behaviors, including period-n orbits, crisis, some chaotic attractors, period-doubling bifurcation to chaos, quasi-period behaviors to chaos, chaos to quasi-period behaviors, bubble and onset of chaos.     

A delay model for viral infection in toxin producing phytoplankton and zooplankton system

An eco-epidemiological delay model is proposed and analysed for virally infected, toxin producing phytoplankton (TPP) and zooplankton system. It is shown that time delay can destabilize the otherwise stable non-zero equilibrium state. The coexistence of all species is possible through periodic solutions due to Hopf bifurcation. In the absence of infection the delay model may have a complex dynamical behavior which can be controlled by infection. Numerical simulation suggests that the proposed model displays a wide range of dynamical behaviors. Different parameters are identified that are responsible for chaos.     

Dynamic complexities in a single-species discrete population model with stage structure and birth pulses

Natural population, whose population numbers are small and generations are non-overlapping, can be modelled by difference equations that describe how the population evolve in discrete time-steps. This paper investigates a recent study on the dynamics complexities in a single-species discrete population model with stage structure and birth pulses. Using the stroboscopic map, we obtain an exact cycle of system, and obtain the threshold conditions for its stability. Above this, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that this the dynamical behaviors of the single-species discrete model with birth pulses are very complex, including (a) non-unique dynamics, meaning that several attractors and chaos coexist; (b) small-amplitude annual oscillations; (c) large-amplitude multi-annual cycles; (d) chaos. Some interesting results are obtained and they showed that pulsing provides a natural period or cyclicity that allows for a period-doubling route to chaos.     

Waves analysis and spatiotemporal pattern formation of an ecosystem model

In this paper, we consider a predator–prey model given by a reaction–diffusion system. This model incorporates Holling-type-II (Michaelis–Menten) and modified Leslie-Gower functional responses. We show the existence of qualitatively different types of system behaviors realized for various parameter values. Our model is investigated with methods of the qualitative theory and the theory of bifurcations. We generalize the traveling waves existence method for populations dynamics with positive derivative densities, to the predator–prey system in which growth densities may change sign. Parallel to this is a discussion and an analysis of alternative model outcomes such as complex pattern formation and spatio-temporal chaos behavior.     

CHAOS IN AN INDIVIDUAL-LEVEL PREDATOR-PREY MODEL

A deterministic predator-prey model describing populations as collections of autonomous individuals was used to investigate population dynamics as an emergent property of individual behaviors and actions in a simulated environment. The model's behavior was clearly chaotic for both the two species interaction and for the prey population alone. Furthermore, estimated parameters from a simple difference equation model fitted to the single-species simulation were nowhere near the chaotic region for the equation. Findings indicate that chaos may very well be characteristic of biological populations despite the findings of several empirical studies in the past, and that chaotic models can be constructed from direct observation of, and experimentation with, biological populations by focusing on individuals and their behaviors, rather than on population parameters.     

Li–Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice

This paper investigates a globally nonlocal coupled map lattice. A rigorous proof to the existence of chaos in the scene of Li–Yorke in that system is presented in terms of the Marotto theorem. Analytical sufficient conditions under which the system is chaotic, and has synchronous behaviors are determined, respectively. The wider regions associated with chaos and synchronous behaviors are shown by simulations. Spatiotemporal chaos, synchronous chaos and some other synchronous behaviors such as fixed points, 2-cycles and 2²-cycles are also shown by simulations for some values of the parameters.