Difference between bifurcation and chaos

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SUMMARY

Bifurcation refers to the phenomenon where waveforms transition from stable periodic states to unstable n-periodic states, which can include chaos. Chaos is characterized by aperiodic waveforms that lack a predictable pattern. The discussion confirms that bifurcation encompasses both periodic transitions and chaotic behavior, with n representing the number of periods in the waveform. Understanding these concepts is crucial for analyzing dynamic systems in mathematics and physics.

PREREQUISITES
  • Understanding of dynamical systems theory
  • Familiarity with periodic and aperiodic waveforms
  • Knowledge of mathematical concepts related to stability and instability
  • Basic grasp of chaos theory
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  • Research the mathematical definitions of bifurcation and chaos in dynamical systems
  • Study the implications of n-periodic waveforms in various applications
  • Explore the role of bifurcation diagrams in visualizing system behavior
  • Learn about the Lyapunov exponent as a measure of chaos
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Mathematicians, physicists, and engineers interested in the behavior of dynamic systems, particularly those studying chaos theory and bifurcation phenomena.

student-engineer
Chaos is when the waveforms become aperiodic. I think bifurcation is the phenomenon inclusive of chaos and in addition, it is also termed for situations in which the waveforms become n-periodic.Does bifurcation include period-n phenomenon as well as chaos? From period-n it means that still the waveform is periodic but the period changes and becomes n, where n can be n=2,3,4,..
Waveforms are still unstable on becoming n-periodic.Is this all correct?Kindly, also tell the difference.
Thanks in advance to all those who would discuss.
 
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@Krylov
Can you also kindly explain.
 

Thread 'uA709 op amp compensation'

Most likely this can only be answered by an "old timer". I am making measurements on an uA709 op amp (metal can). I would like to calculate the frequency rolloff curves (I can measure them). I assume the compensation is via the miller effect. To do the calculations I would need to know the gain of the transistors and the effective resistance seen at the compensation terminals, not including the values I put there. Anyone know those values?
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