Chaotic images---the moths of the Chen attractor

Most of the chaotic attractors I come across have double helix structures. This article is about Chen attractor, which was introduced in 1999 by Chen Guanrong and planting fields to propose alternative chaotic attractors.

The Chen system can be represented by one of the following sets of differential equations:

dx=a* (Y-x)
Dy= (c-a) *x-x*z+c*y
Dz=x*y-b*z

A few more introductions to the chaotic attractor:

1999, Chen Guanrong, et al. in the feedback control of chaotic system, a new chaotic system is found which is equivalent to the non-topological Lorenz system, namely Chen system, which is considered as dual system. with the study of Chaos theory, its application in the field of science and engineering technology has developed rapidly in recent years. Since the concept of driver-response synchronization has been proposed in the early 1990s, the chaotic synchronization methods have been generalized synchronization, synchronization, synchronization, activation control and so on. Because of the potential application value of chaotic synchronization in the fields of secure communication and life science, the research on this subject has aroused people's wide attention. At present, chaotic research is generally based on some typical chaotic systems, and these typical chaotic system models are: Lorenz system, Rossler system, Chua Circuit, duffing oscillator, logistic system, Henon mapping, etc.

Professor Chen Guanrong found a new attractor in the process of studying chaotic anti-control, which is not topological equivalence with Lorenz system and Rossler system, which is called Chen System, which is another typical chaotic system, and also used as a hotspot system for chaotic synchronization research. In addition, the Lorenz system family is also a hotspot of research. With the deepening of the research, many chaotic systems have been born, and the above are only some typical chaotic systems which are widely quoted in the chaotic research.

As to the role of this group of Chen Attractors, I do not care, here is just based on this formula to generate beautiful images.

This generates a chaotic image using the script code of its own definition syntax. Related software see: Ychaos generating chaotic images. If you are interested in a graphic image of students, welcome to join QQ Group: 367752815

First, the script code:

[Scriptlines]u=a* (Y- x) v= (c-a) *x-x*z + c*yw=x*y-b*zx=x+u*ty=y+v*  TZ=z+w*t[variables]a=40.000000b=3.000000c=28.000000  t=0.001000x=-0.100000y=0.500000Z =-0.600000

In the script code, above is the mathematical expression, the following is the initial value of the variable.

From the internet also found a hyper-chaotic Chen Attractor _ sine regulation function its script code is as follows:

[Scriptlines]f=g*z-h*sin (z) u=a* (Y-x) v= (c-a) *x-x*f + c*yw=x*y-b*ZX=x+u*Ty=y+v*TZ=z+w*T[variables]a=40.000000b=3.000000C=28.000000g=1.000000h=5.000000T=0.000100x=-0.100000y=0.500000Z=-0.600000

Related software:

Ychaos Generating Chaotic images

Related articles:

Chen's attractor of chaotic mathematics

Chaotic images---the moths of the Chen attractor