Can subharmonics in a system be also termed as bifurcation?

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Discussion Overview

The discussion centers around the relationship between subharmonics and bifurcation in non-linear systems. Participants explore definitions and characteristics of both concepts, examining whether subharmonics can be classified as a form of bifurcation, particularly in the context of periodic behavior and system dynamics.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that the existence of subharmonics can be considered a form of bifurcation.
  • Others argue that while non-linear systems can exhibit subharmonics, only certain systems, like the Duffing oscillator, demonstrate bifurcations, suggesting that the reverse is not necessarily true.
  • A participant emphasizes the need to define bifurcation and subharmonic, noting that subharmonics arise from energy storage and can be generated by various systems, including digital circuits.
  • There is a discussion about how bifurcations can lead to period doubling or halving, which may relate to subharmonic generation, raising questions about the nature of odd and even subharmonics in this context.
  • Another participant references external sources to support the idea that subharmonic operation at period-n can be classified as bifurcation, indicating a connection between the two concepts.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether subharmonics can be classified as bifurcation. Multiple competing views remain, with some supporting the connection and others challenging it.

Contextual Notes

Definitions of bifurcation and subharmonics are not universally agreed upon, and the discussion highlights the complexity of these concepts in non-linear dynamics. The relationship between periodic behavior and system operation remains unresolved.

student-engineer
I think that the existence of subharmonics is also bifurcation.Is that true
 
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No, I am not even sure why you would think that.
Any non-linear system will have subharmonics; but only certain systems (say a Duffing oscillator) will exhibit bifurcations.
It is obviously true that a bifurcating system will have lots of subharmonics; the the reverse is not true.
 
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student-engineer said:
I think that the existence of subharmonics is also bifurcation.Is that true
You will have to define what you consider to be a bifurcation, the meaning of the term sub-harmonic and what you will consider to be the fundamental or driving function.

Higher harmonics, with frequencies, f * n, are generated by distortion of a waveform due to a non-linearity. Different types of distortion generate odd or even harmonics.

Sub-harmonics with frequencies, f/n, that are lower than the fundamental driving function are generated when there is energy or information storage. For example, a staircase generator, a digital divider or a for-next loop in software can all generate integer sub-harmonics at lower frequencies than the fundamental clock.

Bifurcations can double or halve the period, so they can halve or double the frequency. The entry to chaos is characterised by period doubling which is frequency halving, may be that is sub-harmonic generation. Stability is reached by period halving which is frequency doubling, that may be super-harmonic generation.

A bifurcation is a splitting into two, which seems to qualify some bifurcations as even sub-harmonics. Can bifurcations ever generate odd sub-harmonics?
 
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If the waveform repeats at the multiples of the period T, then such a waveform is subharmonic. This is according to page 1 of the research paper http://ieeexplore.ieee.org/document/124574/
Bifurcation in system occurs when the system deviates from its period-1 regime of operation and starts functioning at period-n. This is according to page 19, section 1.1.4 of the book http://dlx.b-ok.org/genesis/165000/...lex_behavior_of_switching_power(b-ok.org).pdf
From this information, I was concluding that period-n subharmonic operation of the system is also bifurcation
From the information given on the page https://books.google.com.pk/books?i... between subharmonics and bifurcation&f=false
I was concluding the same
 

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