We mentioned previously that chaotic electronic circuits provide an easy way to study chaos.  However, many people don’t have the background or the laboratory facilities needed to build from actual components and then test the chaotic electronic circuits we will be discussing . 

That is not an impediment to the study of chaos since there is an excellent computer program that accurately simulates circuits and displays the responses.  The best part is that this software is available for FREE! 



Virtually all electronic circuit simulation software available today is based on a program called SPICE which was developed at the University of California at Berkeley.  Because SPICE was developed under a government grant, it is in the public domain and is available for all to use.  SPICE was first released to the public in 1972.


The original SPICE program required that the circuit to be analyzed be described by writing a “netlist.”   A netlist consists of circuit defining statements that use a somewhat awkward syntax. 

A number of private companies and universities have since incorporated more friendly user interfaces called “schematic capture” programs with SPICE.  These allow the schematic diagram of the circuit to be drawn on the computer using standard electronic component symbols.  The schematic diagram is then converted effortlessly by the schematic capture program into a netlist that the SPICE program understands. 

Once the netlist for a particular circuit has been generated by the SPICE program, it can be saved and used in subsequent analyses of the same circuit in the future.  Using an already written netlist is easy.  I will make the netlists of some chaotic circuits available for you to use and I will explain how to use them.



Many of the SPICE-based programs available today are either fairly expensive or else lack good support and updating.  An exception is LTspice developed by the Linear Technology Corporation (hence, the “LT” in LTspice).  Ltspice is a registered trademark of Linear Technology Corporation. 

For the benefit of those who are not aware of this, Linear Technology Corporation is one of the major U.S. integrated circuit developers and manufacturers.

The LTspice program is as good as any (and much better than most) of the SPICE-based programs that this author has seen and used.  Best of all, LTspice is completely FREE!



LTspice can be obtained at the following url: 


(Copy and paste this URL into your web browser or click on the blue link below.)




A variety of instruction manuals for LTspice can be found on the internet by Googling “LTspice manual.”   Several of them are available below:

LTspice IV Getting Started Guide

LTspice_Basic Tutorial

LTspice_An Introduction

(Click on these instruction manual titles to read and save them as pdf files.)




An excellent LTspice user group can be found at the following url:



A direct link to this LTspice user group is

LTspice Group

I’ve been amazed at how knowledgeable and helpful the members of this user group are and how quickly they respond to questions. 



LTspice comes with an extensive library of electrical component models for resistors, capacitors, inductors, diodes, and transistors.  You will not have to add any more of these types of component models to its library to perform the simulations described on this website. 

There is, however, an integrated circuit model that is not included in the LTspice library that you may want to add.  This is the model for the general purpose TL082 op-amp

LTspice comes with several Linear Technology general purpose op-amps which are basically similar to the TL082 and which are perfectly fine to use in simulating any of the chaotic circuits we will discuss.  Examples of very good Linear Technology general purpose op-amps are the LT1057 and the LT1113.  

However, I recommend to those who plan to actually build the chaotic circuits which call for op-amps other than the TL082 to consider using the TL082 op-amp as a substitute.  The chaotic circuits we will discuss USUALLY are not fussy about the op-amps used. 

The TL082 is widely available, easy to work with, and is very inexpensive .  You then likely will want to use the TL082 in your LTspice simulations as well. 

If you search the internet for information concerning how to add a new integrated circuit to the LTspice library, you will find several different ways of doing this.  One very good way is the method suggested by the experts at Linear Technology.  You can click on the following link for that information:


Another, equally good set of instructions for adding new models to LTspice is also included below.  It was developed by Professor Bob York of the Electrical and Computer Engineering Department at the University of California, Santa Barbara.  In his discussion, he covers adding new models to both Orcad Pspice as well as to LTspice.  You need only learn the method that pertains to LTspice.  It is extremely well written. 


You will need to have the Spice netlist for the model you want to add.  Why not do a Google search for the Spice netlist and then, to give yourself practice, create the new component files as the instructions above describe. 

If you are an LTspice beginner and this sounds a bit intimidating to you, you can click-on, copy, and save the following files into a new folder that you  will use for new LTspice components.





The  TL082.sub  file above is the subcircuit file for that device.  It actually is the Spice netlist for the device but when it has a  .sub  extension, LTspice recognizes it as a subcircuit file.  The  TL082.asy  file is the component symbol file for that device.

When you click-on and save these files, they will be saved as text files with a  .txt  file extension because both are actually text files.  Make sure that when you save these files, the  .txt  extension is  removed.  You want to end up with the files   TL082.sub  and  TL082.asy  Then follow Professor Yorke’s instructions for adding these files to the LTspice component library.



I urge you to download LTspice and become familiar with its use.  Do the examples shown in the instruction manuals listed above and in other LTspice tutorials available on the internet.  Like with anything else, you need to practice using LTspice to become proficient in its use.