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student-engineer
What is the best software for the analysis of chaos in electric circuits.
Yes,I am familiar with them.But isn't chaos analysis done by simulating the differential equation or difference equations for a system.May be SPICE analysis is also possible but for that,may be some value is varied such as inductance and the system has a closed loop voltage or current control.Why is chaos analysis done with circuits which have closed loop control?I have simulated circuits in SPICE.It is an easy software,but how to do chaos analysis on it?berkeman said:Most SPICE packages could be used. Are you familiar with any SPICE packages?
Attached is a spice simulation of Chua's circuit.student-engineer said:I have simulated circuits in SPICE.It is an easy software,but how to do chaos analysis on it?
Thank you.Baluncore said:Attached is a spice simulation of Chua's circuit.
Remove the .txt extensions to run the .asc file in LTspice.
Which software can be used for analysis if I make state space representation of the circuit?berkeman said:I'm not that familiar with Chaos Theory https://en.wikipedia.org/wiki/Chaos_theory
And SPICE does use differential equations for part of the modeling. The disadvantage is that it takes a long time to accurately simulate many time-domain waveforms, and you might be able to use a different type of simulation to speed things up (like using a State Space model)...
There is some code here that might help.student-engineer said:Which software can be used for analysis if I make state space representation of the circuit?
Yes, since the differential equation is the mathematical model that describes the dynamics of the circuit.student-engineer said:But isn't chaos analysis done by simulating the differential equation or difference equations for a system.
Thank you.Krylov said:Yes, since the differential equation is the mathematical model that describes the dynamics of the circuit.
Here follow some other remarks that I hope you will find helpful.
In addition to pure simulation, it is often useful to perform a numerical continuation analysis. This typically begins by selecting a system parameter and watching how simple invariant sets (such as equilibria and limit cycles) (dis)appear or change their stability at bifurcation points. A rather user friendly MATLAB package for this purpose that has seen frequent use in research is MatCont. The corresponding literature reference is:
While simulation can show you chaos, continuation and bifurcation analysis can provide insight into how a system may become chaotic in the first place.
- Dhooge, A., Govaerts, W. and Kuznetsov, Yu. A. MATCONT: a MATLAB package for numerical bifurcation analysis of ODEs. ACM Trans. Math. Software 29 (2003), no. 2, 141–164.
For the Chua circuit in particular, you could have a look at the end-of-chapter project (Section 16.5) in the second edition of Differential Equations, Dynamical Systems and an Introduction to Chaos by Hirsch, Smale and Devaney. (Meanwhile, there is a third edition, but as far as I could see, the section numbering did not change for this particular section.) This project - together with the material in that chapter - will help you understand how chaos in Chua's circuit relates to Shil'nikov's homoclinic bifurcation.
In case you cannot (or: don't want to) get the book, here are the two literature references that the project cites on Chua's circuit:
This and related systems have been the subject of intense study, so the above is just a start. A lot more can be found if you look for it. Have fun!
- Chua, L., Komuro, M., and Matsumoto, T. The double scroll family. IEEE Trans. on Circuits and Systems. 33 (1986), 1073.
- Khibnik, A., Roose, D., and Chua, L. On periodic orbits and homoclinic bifurcations in Chua’s circuit with a smooth nonlinearity. Int. J. Bifurcation and Chaos. 3 (1993), 363.
Chaos analysis in electric circuits is a branch of study within electrical engineering and physics that focuses on the behavior of nonlinear systems. It involves examining the complex and seemingly random patterns that can arise in the behavior of electrical circuits, which can have important implications for understanding and controlling their behavior.
Software is crucial for chaos analysis in electric circuits because it allows for precise and accurate analysis of complex systems. With the help of software, scientists and engineers can simulate and analyze circuits in a controlled environment, which can provide valuable insights into their behavior and help in making predictions and designing more efficient and reliable systems.
Some of the most commonly used software for chaos analysis in electric circuits include MATLAB, Simulink, PSpice, and LTSpice. These programs offer a wide range of tools and features for simulating and analyzing electrical circuits, making them popular choices among scientists and engineers.
Choosing the best software for chaos analysis in electric circuits depends on your specific needs and goals. Consider factors such as the complexity of your circuit, the type of analysis you need to perform, and the availability of tutorials and support when making your decision. It is also helpful to read reviews and compare features of different software options.
While software is a powerful tool for chaos analysis in electric circuits, it is possible to perform some level of analysis without it. However, this often requires advanced mathematical knowledge and a deep understanding of the circuit's behavior. Using software can save time and effort and provide more accurate results for complex systems.