﻿ 一类双稳系统的动力学性质及其在林业工程上的应用 Dynamic Properties of Bistable System and Its Application in Forestry Engineering

Dynamical Systems and Control
Vol.05 No.04(2016), Article ID:18848,8 pages
10.12677/DSC.2016.54016

Dynamic Properties of Bistable System and Its Application in Forestry Engineering

Xiao Lin, Chunrui Zhang*

Department of Mathematics, Northeast Forestry University, Harbin Heilongjiang

Received: Sep. 30th, 2016; accepted: Oct. 28th, 2016; published: Oct. 31st, 2016

ABSTRACT

The unstable point in the bistable system plays a decisive role and acts as a threshold in image enhancement. Under certain conditions, let the unstable point (that is, the threshold) tend to a stable point in order to achieve the image enhancement. In this paper, a class of bistable systems is studied and the linear stability of the system is analyzed. By using this property, the image histogram equalization is realized by traversing each pixel value at the special time point. Better results.

Keywords:Image Enhancement, Bistable System, Pixel Value, Histogram Equalization

1. 引言

2. 双稳系统简介

(1)

Figure 1. The bifurcation diagram

Figure 2. Bistable potential function

3. 一个双稳系统的线性稳定性分析

(2)

②当平衡点为时线性化后得到系统(1)的特征方程为：

③当平衡点为时，在此平衡点处线性化后得到系统(1)的特征方程为：

(3)

I. 数字图像m ´ n的每一个点(I,j)为一个像素值，把像素值作为初值，也就是输入值，原图像就是输入图像，像素值构成的矩阵为输入矩阵；

II. 通过双稳系统输出方程的解，遍历图像的每一个点，从第一行第一列到第m行第n列，使每一个点都经过双稳系统，每一个点都会有一个输出解，这样就会得到一个与原图像行与列相同的矩阵，作为输出矩阵；

III. 将输出矩阵生成新图像。

Figure 3. Solution curve: Four initial value

4. 木材缺陷图像增强

Figure 4. Before and after the image progress and its corresponding histogram

Figure 5. tspan =2 and 8 output image and its histogram

Figure 6. The relationship between the time t and the difference between the solutions under the initial value

5. 结论

Dynamic Properties of Bistable System and Its Application in Forestry Engineering[J]. 动力系统与控制, 2016, 05(04): 143-150. http://dx.doi.org/10.12677/DSC.2016.54016

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