This paper is primarily concern with the formulation and analysis of a reliable numerical method based on the novel alternating direction implicit finite difference scheme for the solution of the fractional reaction–diffusion system. In the work, the integer first‐order derivative in time is replaced with the Caputo fractional derivative operator. As a case study, the dynamics of predator–prey model is considered. In order to provide a good guidelines on the correct choice of parameters for the numerical simulation of full fractional reaction–diffusion system, its linear stability analysis is also examined. The resulting scheme is applied to solve both self‐diffusion and cross‐diffusion problems in two‐dimensions. We observed in the experimental results a range of spatiotemporal and chaotic structures that are related to Turing pattern. It was also discovered in the simulations that cross‐diffusive case gives rise to spatial patterns faster than the diffusive case. Apart from chaotic spiral‐like structures obtained in this work, it should also be mentioned that Turing patterns such as stationary spots and stripes are obtainable, depending on the initial and parameters choices. 相似文献
This paper proposes a new method for eliminating impulse noise. Based on the space characteristic of object and noise, three kinds of basic noise patterns are introduced to describe noise and detect noise candidates. Correspondingly, noise removal operators are presented to remove the impulse noise. Extensive experiment results have shown that the proposed method is better than some of the state-of-the-art methods. 相似文献
Currently surrogate data analysis can be used to determine if data is consistent with various linear systems, or something else (a nonlinear system). In this paper we propose an extension of these methods in an attempt to make more specific classifications within the class of nonlinear systems.
In the method of surrogate data one estimates the probability distribution of values of a test statistic for a set of experimental data under the assumption that the data is consistent with a given hypothesis. If the probability distribution of the test statistic is different for different dynamical systems consistent with the hypothesis, one must ensure that the surrogate generation technique generates surrogate data that are a good approximation to the data. This is often achieved with a careful choice of surrogate generation method and for noise driven linear surrogates such methods are commonly used.
This paper argues that, in many cases (particularly for nonlinear hypotheses), it is easier to select a test statistic for which the probability distribution of test statistic values is the same for all systems consistent with the hypothesis. For most linear hypotheses one can use a reliable estimator of a dynamic invariant of the underlying class of processes. For more complex, nonlinear hypothesis it requires suitable restatement (or cautious statement) of the hypothesis. Using such statistics one can build nonlinear models of the data and apply the methods of surrogate data to determine if the data is consistent with a simulation from a broad class of models. These ideas are illustrated with estimates of probability distribution functions for correlation dimension estimates of experimental and artificial data, and linear and nonlinear hypotheses. 相似文献
Because of the complicated geometry of the slotted structure, analytical theories of such structures are inevitably developed
on the basis of simplifying assumptions. On the other hand, the accuracy of the theory is of importance to the design of microwave
interaction structures. In this study, modes of the slotted waveguide are investigated analytically and simulated with the
HFSS code. It is shown that, in spite of the approximations made, the dispersion relation and field patterns of the standard
analytical theory are in excellent agreement with the HFSS simulations over the complete range of the slot depth. Modes not
built into the theory will also be noted. 相似文献
Summary The Ginzburg-Landau modulation equation arises in many domains of science as a (formal) approximate equation describing the
evolution of patterns through instabilities and bifurcations. Recently, for a large class of evolution PDE's in one space
variable, the validity of the approximation has rigorously been established, in the following sense: Consider initial conditions
of which the Fourier-transforms are scaled according to the so-calledclustered mode-distribution. Then the corresponding solutions of the “full” problem and the G-L equation remain close to each other on compact intervals
of the intrinsic Ginzburg-Landau time-variable. In this paper the following complementary result is established. Consider
small, but arbitrary initial conditions. The Fourier-transforms of the solutions of the “full” problem settle to clustered
mode-distribution on time-scales which are rapid as compared to the time-scale of evolution of the Ginzburg-Landau equation. 相似文献
A method for generating a high visibility digital speckle shearing fringe pattern is proposed. A three-step phase shifting technique which involves the introduction of arbitrary phases is utilized. The phase shifting technique is carried out using a rotating mirror and a theoretical model which involves a linear correlation algorithm is discussed. Experimental results showing correlation fringe patterns and a deformation phase map are presented. 相似文献