内在随机性

本文首先分析了混沌含义的演变和混沌的三个本质特征：内在随机性、对初值的敏感性和混沌序。

At the outset , the article analyses the evolution of the meaning of chaos and its three intrinsic characteristics : inner randomness , sensitivity to initial value and " chaos order " .

分岔、混沌、奇怪吸引子、湍流及其它&关于确定论系统中的内在随机性

Bifurcation , chaos , strange attractor , turbulence and all that . & on intrinsic stochasticity in deterministic systems

变尺度混沌优化（MSCOA）是一种改进的混沌优化方法（COA），利用混沌运动的内在随机性、遍历性和规律性进行全局寻优；

Mutative scale chaos optimization algorithm ( MSCOA ) is a modified chaos optimization algorithm ( COA ), which possesses the properties of randomness , ergodicity and regularity of chaos movement .

台风运动内在随机性的研究

Study of the randomness inherent in the movement of a typhoon

混沌是确定性非线性动力系统内在随机性的表现。

Chaos is internal random behavior expression of certainty nonlinear dynamical system .

确定论动力学系统的内在随机性

Intrinsic Randomicity of Dynamics System of Determinate Theory

一般算在量子力学头上的内在随机性，其实正是这个外加假定的结果。

The intrinsic randomness commonly ascribed to quantum mechanics is the result of this postulate .

结果表明模式大气中台风中心的移动具有内在随机性。

Results show that there exists randomness inherent in the center movement in the model atmosphere .

利用混沌变量特定的内在随机性和遍历性，建立了简单混沌优化算法。

An chaos algorithm is established by use of the intrinsic stochastic property and ergodicity of chaos movement .

一般而言，混沌是指在确定性的系统中，不需要附加任何随机因素亦可出现的类似随机的动力学行为（内在随机性）。

In general , chaos means a random-like behavior ( intrinsic randomness ) in deterministic systems without adding any stochastic factors .

另外，本文作为非线性系统在一定参数范围内所表现出的内在随机性已经渐渐受到更多的学者的关注。

Moreover , the inner random displayed at the range of parameters for nonlinear systems has been made to attract more attention .

历史作为一个复杂系统可能的内在随机性的混沌状态并不少见。

It is common that the history , as a complicated system , presents the possible confusion of " inherent randomness " .

混沌学中的内在随机性对经济发展道路多样性的启示：欧洲中心论的局限

The Enlightenment of " Inherent Randomness " of Chaos Theory to the Diversity of Economic Development Paths : Limitation of the Eurocentric Approach

通过分析，认识到土体附加应力系统是集外在随机性、确定性、内在随机性于一身的复杂、非线性系统。

We waked up to that additional stress system of mass is a complex and nonlinear system with credibility , randomicity and internal randomicity .

混沌系统有很好的保密通信特性，比如内在随机性、对初值和参数的极端敏感性等等。

The chaotic system has nice characteristic of secure communication , such as randomness , the extreme sensitivity to the parameter and the initial value .

建筑和城市的演化具有初值敏感性、分岔、内在随机性、奇怪吸引子、自相似等特性。

The evolution of architecture and city have a lot of characteristics which include sensitivity to initial condition , separate , randomness inherent , strange attractors and self-similar .

引入了混沌算子，利用混沌变量的特定内在随机性和遍历性来跳出局部最优点，有效地克服了传统遗传算法的早熟的缺点。

By introducing the Chaos Operator , it has overcome the defect of precocity for SGA , for its particularly inherent randomness and ergodicity to skip the partial optimization .

利用混沌运动的遍历性、内在随机性、规律性等特点，结合MATLAB5.3.1高级程序设计语言的优化工具箱，提出了一种混沌约束优化算法。

By the use of the properties of ergodicity , inherent stochastic property and regularity of chaos , a chaos optimization algorithm is proposed with the help of the optimization Toolbox of Matlab 5.3.1 programming language .

混沌系统的一些特性，如初值敏感性、内在随机性、拓扑传递性等特性，同密码学中对加密系统的原则（扩散、混淆）有着密切的关系。

Some features of chaotic systems , such as sensitive dependence on initial conditions , inherent randomness and topological transitivity , are closely related to the principle of encryption systems ( diffusion , confusion ) in cryptography .

该算法利用混沌变量的特定内在随机性和遍历性对基因座空间进行搜索，有效地克服了遗传算法容易收敛于局部最优的缺点，大大提高了遗传算法的寻优速度。

Based on the stochastic and ergodic property of chaos variables , the method searches the space of loci , which effectively overcomes the drawback of converging to local optimization and greatly improves the speed of searching the optimum .

混沌理论适合描述确定性非线性系统的内在随机性，具有对初始条件敏感，遍历性、规律性等特点，作为确定论和概率论的桥梁，其特性符合电力系统负荷预测的内在要求。

Chaos theory can demonstrate the inherent randomness of a deterministic nonlinear system . As the bridge of deterministic and stochastic manner , it has the characteristics of the sensitivity to initial conditions , ergodicity , orderliness and so on .

把多群体伪并行进化的并行性和混沌运动的内在随机性结合起来，利用不同的混沌扰动策略，把混沌变尺度映射机理应用到种群初始化和中间群体的优化进化实现函数优化。

Combines the parallel character of multiple population pseudo parallel evolution with inner stochastic character of chaos movement , applying different chaotic disturbance strategies , taking chaos ' variable measure map mechanism into population initialization or middle populations fulfilled function optimization .

其基本思想是在原搜索区域的基础上，根据每次寻优的结果自适应的调整搜索空间，逐步缩小搜索区域，并利用混沌变量的内在随机性和遍历性跳出局部最优点，最终获得最优解。

The main idea is self-adapting adjust search space according to the results of each optimization , and takes use of the randomicity and ergodicity properties of the chaos to break away the local optima , and ultimately finds the global optima .

该模型既考虑了矿震系统的非线性动力学本质，又利用胞映射理论消除了初值的随机性和矿震系统本身的内在随机性对预测结果的影响。

The nonlinear dynamic essences of mine quake is considered by the model , and the influences of random of initialized values of variables and the internal randomicity of mine quake on forecasting results are subtly eliminated with the cell mapping theory .

利用混沌迭代的遍历性和内在随机性，提出三种混沌免疫优化组合算法，以弥补免疫进化算法收敛性能差的缺陷。

On the basis of the ergodicity and internal randomicity of the chaos iteration , three types of novel Chaos Immune Optimization Combinational Algorithms ( CIOCA ) were presented to solve the problem of poor convergence of the Immune Evolutionary Algorithm ( IEA ) .

考虑到因确定性系统的外在随机因素和内在随机性所造成的长期预报的不准确性，我们将有关的浑沌理论和数理统计理论结合起来，提出了d维相空间模回归预报法。

Considering the error of long-term forecast , which is caused by the external ran-dom factors and the internal randomness of a deterministic system , the theory about chaos is combined with statistics theory in this paper , then a modular regression model of d-dimensions phase space is set up .

基于混沌运动的遍历性、内在的随机性、“规律性”等特点的混沌优化算法是一种有效的全局优化算法，其计算复杂度较低。

Based on the properties of ergodicity , stochastic property and " regularity " of chaos , the chaos optimization method can get global solution with low computational load .

由于混沌系统具有内在的随机性和对初值的敏感性等特点，使其被广泛的应用于保密通信、信号处理、图像处理等方面。

Because such chaotic systems progress certain features , such as high randomicity and hyper sensitivity to initial conditions , the application of chaos can be especially found in secure communications , signal progressing and image progressing etc. Chaos synchronization has become the key technique in secure communications .

混沌优化方法利用混沌运动特定的内在遍历性、随机性和规律性等特点跳出局部最优点，接近最优点；

By use of the properties of intrinsic ergodicity , stochastic property , and regularity of chaos , the chaos optimization algorithm can escape from the local minima and approach the global minima .

分形与混沌理论的研究与发展，揭示了自然界中一大类无规几何形体物理过程的内在规律性及其动力演化过程的内在随机性。

With the studies and developments on fractals and chaotic theory irregularity on geometrics and the inherent stochasticity of dynamical evolution of a big class of natural phenomena have been revealed .