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Zeno Behaviour or Zeno Phenomenon can be informally stated as the behavior of a system making an infinite number of jumps in a finite amount of time.

While this is an important Control system problem in ideal systems, can Zeno behavior exist in real systems? Any examples?
If so, why don't noise or external factors deviate a system from achieving Zeno?

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    $\begingroup$ If a bouncing ball is simulated in a physics engine, there is a delay between the steps. This delay is the quantum zeno effect. It is unclear if the ball on the old or on the new position. Related: [robotics.stackexchange.com/questions/2812/… $\endgroup$ Aug 18, 2016 at 22:04
  • $\begingroup$ @ManuelRodriguez , I think the Zeno behaviour I defined is quite different from the Zeno Effect that you have mentioned. My references are limited but I have learnt Zeno Behaviour here: coursera.org/learn/mobile-robot/lecture/IsnqW/… $\endgroup$
    – nikpod
    Aug 19, 2016 at 5:40
  • $\begingroup$ @nikelpod: I have learned the Zeno behavior from Alan Turings unpublished paper of 1954 ;-) $\endgroup$ Aug 19, 2016 at 18:57
  • $\begingroup$ If I may be so bold, is zeno's paradox not a sufficient answer? or are you asking specifically about reactive systems that depend on a (for lack of better term) zeno event to provide feedback and infinite number of times. $\endgroup$
    – tuskiomi
    Aug 5, 2019 at 19:55

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To the principal question, "can Zeno behavior exist in real systems?" the answer is no.

Real systems don't do any infinite anything. The Quantum Zeno Effect, a.k.a. Turing paradox, is a purely quantum phenomenon. In this robotics forum, real systems are macroscopic, and macroscopic systems don't do any quantum anything. Hence, there are no examples and no need to explain about noise.

If you want to get all reductionist and want to explain how macroscopic phenomena arise from quantum behavior, or how the infinities and/or infinitesimals of differential equations are used to describe real behavior, I'll have to send you to some other StackExchange site.

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